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

1. 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

2. 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.

3. 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.”

4. Starks et al., 2008

5. 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”

6. Helliwell’s 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

7. 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.

8. 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.

9. Introducing Inhomogeneous Ionosphere Profile

10. 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%.

11. 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 = λ﬩ Width = ½ λ﬩ Resonant Striation Width: (n is integer) Eliasson and Papadopoulos, 2008

12. Whistler Wave Propagation through Striations with 8 m Width Density Low-Hybrid E Whistler Wave B 90 km 150 km 210 km

13. Whistler Wave Propagation through striations with 8 m width T =1.2 ms Amplitude increase due to slow down of whistler wave

14. Whistler Wave Propagation through striations with 8 m width Without mode conversion With mode conversion 16 dB Loss

15. Simulation with Non-Uniform Density: 2m striation width Density Low-Hybrid E Whistler Wave B 90 km 120 km 150 km

16. Whistler Wave Propagation through striations with 2 m width Without mode conversion With mode conversion

17. Whistler Wave Propagation through striations with 15 m width Without mode conversion With mode conversion

18. 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

19. 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

20. 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.

21. Simulation with uniform density and without collisions Low-Hybrid E Whistler Wave Magnetic Field

22. Simulation with uniform density and ion/neutral collisions Low-Hybrid E Whistler Wave Magnetic Field