Damping of Whistler Waves through Mode Conversion to Lower Hybrid Waves in the Ionosphere

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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

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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.

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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.
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Starks et al., 2008
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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

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Helliwells whistler wave absorption model due to
electron-neutral collision
20 kHz
Day Time
2 kHz
20 kHz
Use interpolation for other
frequencies
Night Time
2 kHz
Helliwell, 1965
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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.

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Modeling Whistler Wave and Lower Hybrid Wave
Conversion
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.

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Introducing Inhomogeneous Ionosphere Profile
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Simulation Set-up
Periodic B.C.
Non-Uniform electron density Whistler wave
frequency 18 kHz
120 m
120 km
150 km
90 km
B field
300x1200 grids
Density Striation Gaussian shape with width
2m, 8m and 15 m, respectively. Density deviation
5.
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Striation width plays an importance role
LH Wave
Striation width for resonant LH-whistler
conversion for wave frequency f 18 kHz
Whistler Wave
Resonant Mode Conversion
Width ??
Width ½ ??
Resonant Striation Width
(n is integer)
Eliasson and Papadopoulos, 2008
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Whistler Wave Propagation through Striations with
8 m Width
Density
Low-Hybrid E
Whistler Wave B
90 km
150 km
210 km
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Whistler Wave Propagation through striations with
8 m width
T 1.2 ms
Amplitude increase due to slow down of whistler
wave
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Whistler Wave Propagation through striations with
8 m width
Without mode conversion
With mode conversion
16 dB Loss
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Simulation with Non-Uniform Density 2m striation
width
Density
Low-Hybrid E
Whistler Wave B
90 km
120 km
150 km
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Whistler Wave Propagation through striations with
2 m width
Without mode conversion
With mode conversion
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Whistler Wave Propagation through striations with
15 m width
Without mode conversion
With mode conversion
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Comparison of Whistler Wave Attenuation Factors
Whistler-LH Wave Conversion with 8 m striation
width
Whistler-LH Wave Conversion with 15 m striation
width
Electron-Neutral Collision
2 m striation width
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Whistler Wave Propagation through striations with
mixed width
Density
Without mode conversion
With mode conversion
Low-Hybrid E
Whistler Wave B
10 dB
90 km
120 km
150 km
Striation width varies from 2 to 10m
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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.

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Simulation with uniform density and without
collisions
Low-Hybrid E
Whistler Wave Magnetic Field
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Simulation with uniform density and ion/neutral
collisions
Low-Hybrid E
Whistler Wave Magnetic Field