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