Damping of Whistler Waves through Mode Conversion to Lower Hybrid
Waves in the Ionosphere
X. Shao, Bengt Eliasson, A. S. Sharma, K. Papadopoulos, G. Milikh
Dept. of Physics and Astronomy, Univ. of Maryland
Background• The VLF waves excited by powerful ground-based
transmitter propagate in the Earth-ionosphere waveguide and leaks through the ionosphere to the magnetosphere.
• Recent studies [Starks et al. 2008] using combined Earth-ionosphere waveguide model and ray-tracing model found that the model systematically overestimates the VLF wave field strength in the plasmasphere owing to VLF transmitter by 20 dB at night and 10dB during the day.
• We present a numerical model to simulate linear mode conversion between whistler wave and lower hybrid wave due to the interaction with short scale density striations such as field-aligned irregularities in the Earths ionosphere.
• We study the damping of whistler wave due to this mode conversion.
Starks et al., 2008: The 20 dB loss problem
“Helliwell Absorption Model, VLF ionospheric absorption curves from Helliwell [1965, Figures 3 –35]; approx-Helliwell, daytime VLF absorption curves using night Helliwell values plus 26 dB.”
Starks et al., 2008
Starks et al., 2008: The 20 dB loss problem
• “Given that the models all agree at 150 km, and that the satellite data shows similar error whether taken directly above the transmitter at 600, 1500 or 7000 km, or conjugate to it at the end of a very long inter-hemispheric propagation path, it is clear that the ‘‘missing power’’ is lost somewhere in the ionosphere.”
• “Possible candidates for loss processes include enhanced D region reflectivity due to transmitter modification, scattering from transmitter-induced irregularities, and conversion to nonpropagating lower hybrid modes.”
• Current Fixes: “a simple constant correction factor, adjusting our initial conditions downward by 23 dB at night and 10 dB during the day (with no changes to the added noise floor).”
• “Additional focused research into the transionospheric propagation of whistler mode VLF radiation is clearly needed”
Helliwell’s whistler wave absorption model due to electron-neutral collision
2/12/3|)cos(|2
e
pe
c
1
0
31069.8h
hdhA
Use interpolation for other frequencies:
fNight Time
Day Time
2 kHz
20 kHz
2 kHz
20 kHz
Helliwell, 1965
Models to account for 20 dB Loss
• Mishin et al., 2010: Nonlinear VLF effects (parametric instabilities)
• Bell et al., 2008: Plasma density irregularities for linear mode conversion
Possible Models:
• Ganguli et al., 2010: Three Dimensional Whistler Turbulence.
Modeling Whistler Wave and Lower Hybrid Wave Conversion
LHinJ
))](([)1( 02122
wenwLHstreee
w jBjEnm
e
t
j
Linked through striation
• Formulation by Eliasson and Papadopoulos, 2008• Two equations to describe the evolution of whistler and LH wave.• Coupling linked through gradients provided by density striations.• Include inhomogeneous ionosphere.• Collisions can be taken into account.
101
102
103
104
105
90
100
110
120
130
140
150
160
170
Collision Frequency (Hz)
Alt
itu
de
(km
)
Ion-Neutral Collision Frequency
Electron-Neutral Collision Frequency
Introducing Inhomogeneous Ionosphere Profile
1010
1011
1012
90
100
110
120
130
140
150
160
170
Electron Density (1/m3)
Alti
tude
(km
)
Simulation Set-upNon-Uniform electron density Whistler wave frequency = 18 kHz
Density Striation: Gaussian shape with width = 2m, 8m and 15 m, respectively.Density deviation: 5%.
120 m
Periodic B.C.
B field90 km 120 km 150 km
300x1200 grids
100 120 140 1600
5
10
15
20
25
30
Re
so
na
nt
Str
iati
on
Wid
th (
m)
Altitude (km)
LH Wave :
Whistler Wave :
Resonant Mode Conversion :
Striation width plays an importance role
Striation width for resonant LH-whistler conversion for wave frequency f = 18 kHz
Width = ½ λ+
Width = λ+
2/nDstr Resonant Striation Width:
(n is integer)
Eliasson and Papadopoulos, 2008
Whistler Wave Propagation through Striations with 8 m Width
90 km 150 km 210 km
Whistler Wave B
Low-Hybrid E
Density
90 100 110 120 130 140 1500
1
2
3
4x 10
-14
Z (km)
Wh
istl
er
Wa
ve
En
erg
y
90 100 110 120 130 140 1500
1
2
3
4
5x 10
-14
Z (km)
Lo
we
r H
yb
rid
Wa
ve
En
erg
y
No Coll. and M. C.
With M.C. and No Coll.With M.C. and Coll.
No Coll. and M. C.With M.C. and No Coll.With M.C. and Coll.
Whistler Wave Propagation through striations with 8 m width
Amplitude increase due to slow down of whistler waveT =1.2 ms
Whistler Wave Propagation through striations with 8 m width
Without mode conversion
With mode conversion
16 dB Loss
Simulation with Non-Uniform Density: 2m striation width
90 km 120 km 150 km
Whistler Wave B
Low-Hybrid E
Density
Whistler Wave Propagation through striations with 2 m width
Without mode conversion
With mode conversion
Whistler Wave Propagation through striations with 15 m width
Without mode conversionWith mode conversion
80 90 100 110 120 130 1400
2
4
6
8
10
12
14
16
18
20
Z (km)
Wh
istl
er
Wa
ve
Att
en
u. (d
B)
Comparison of Whistler Wave Attenuation Factors
Electron-Neutral Collision
Whistler-LH Wave Conversion with 8 m striation width
Whistler-LH Wave Conversion with 15 m striation width
2 m striation width
Whistler Wave Propagation through striations with mixed width
90 km 120 km 150 km
Without mode conversion
With mode conversion
Density
Striation width varies from 2 to 10m
~ 10 dB
Low-Hybrid E
Whistler Wave B
Summary
• At the altitudes between 90 to 150 km in the ionosphere, the energy of whistler wave energy can be converted to the lower hybrid wave and the lower hybrid wave can be subsequently damped by ion-neutral collisions.
• Striation width plays an important role in Whistler-LH wave conversion efficiency.
• With 2 to 10 m mixed striation width (5 striations within 120 m column), the whistler wave can be attenuated by ~ 10dB, propagating from 90 to 160 km.
• Need further experimental and observational investigations on striation width statistics and whistler wave and lower Hybrid wave conversion.
Simulation with uniform density and without collisions
Low-Hybrid E
Whistler Wave Magnetic Field
Simulation with uniform density and ion/neutral collisions
Low-Hybrid E
Whistler Wave Magnetic Field
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