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Subionospheric VLF propagation

Subionospheric VLF propagation. Prepared by Morris Cohen, Benjamin Cotts, Forrest Foust Stanford University, Stanford, CA IHY Workshop on Advancing VLF through the Global AWESOME Network. Radio waves on the ionosphere. Magnetosphere. Ionosphere. Microwave. MF-HF Waves. LF Waves.

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Subionospheric VLF propagation

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  1. Subionospheric VLF propagation Prepared by Morris Cohen, Benjamin Cotts, Forrest Foust Stanford University, Stanford, CA IHY Workshop on Advancing VLF through the Global AWESOME Network

  2. Radio waves on the ionosphere Magnetosphere Ionosphere Microwave MF-HF Waves LF Waves Atmosphere Earth N. Lehtinen

  3. Ideal parallel-plate waveguide Isotropic Ionosphere Perfect Reflections (reflection coefficient is 1) Ionosphere Reflection Height Transmitter Receiver Earth Perfect Reflections Flat Earth

  4. Basic waveguide analysis Propagation Ionosphere Transmitter Receiver Earth ~80 km Fields within waveguide Modal components of propagating waves Magnetic Field (B) Transverse Electric (TE) Transverse Magnetic (TM) Transverse Electromagnetic (TEM) Electric Field (E) Vertical direction Azimuthal direction All Frequencies Radial direction (propagation) Above ~1.8 kHz Below ~1.8 kHz

  5. Typical Spectrogram TE and TM Weak TEM TEM Wave

  6. Typical conductivities Nighttime Ionosphere Daytime Ionosphere  = 10-7 to 10-5 S/m ~80-90 km ~70-75 km Salt water  = 4 S/m Dry soil  = 10-4 to 10-2 S/m Fresh water  = 10-2 S/m Wet soil  = 10-3 to 10-2 S/m

  7. Basic plasma conductivity Electron response e- e- e- e- e- e- e- e- e- e- e- e- e- e- Applied electric field e- e- Polarization field e- e- e- e- • Applied electric field forced rearranging of electrons • Polarization opposes field, shields it from propagating further • Characteristic plasma response time ~ 1/p • p2 ~ Ne Debye Shielding

  8. Ionospheric Conductivity 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 y x

  9. Mode conversion • Incident fields are “rotated” by electron response • TE and TM waves can be converted into each other Reflected Wave Incident Wave Mixed TM and TE wave Pure TM wave

  10. Anisotropic Conductivity • Direction of wave incidence matters • Different reflection coefficients Reflected Wave Incident Wave Incident Wave Reflected Wave

  11. Reflection coefficients Sharp ionospheric boundary E E k k E k k E Perpendicular incidence Parallel incidence Perpendicular reflection Parallel reflection

  12. Example

  13. The Effect of Collisions • Electrons lose energy via collisions • Electron-neutral collisions are most prominent • Wave energy can be absorbed via collisions

  14. 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 Magnetic Field p= c Dominated by Collisions

  15. Ionospheric Parameters • Measures how strongly electron density affects wave propagation • Measures how strongly geomagnetic field affects wave propagation • Measures how strongly electron-neutral collisions affect wave propagation

  16. Plasma Terms • 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 X=1 X=Z

  17. Conductivity Tensor

  18. Ionospheric Changes Nighttime Ionosphere Daytime Ionosphere Scattered Wave Reflected Wave ~80-90 km ~70-75 km Incident Wave Mode conversion Receiver Transmitter Earth

  19. Refractive Index • 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 B

  20. Ionospheric Absorption • “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)

  21. 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

  22. Attenuation by Frequency From Barr et al. [2000]

  23. 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.

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