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Theoretical modelling of HF heating and resultant ELF/VLF radiation of the auroral electrojet

Explore the generation of ELF/VLF waves through high-frequency heating, analyzing processes such as electron-molecule interactions, ionization, and wave propagation dynamics. Understand the impact of HF facilities like HAARP, emphasizing conductivity modulation and open research questions. Investigate the significance of electron distributions on atmosphere heating and wave propagation, highlighting the role of self-consistent HF fields.

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Theoretical modelling of HF heating and resultant ELF/VLF radiation of the auroral electrojet

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  1. Theoretical modelling of HF heatingand resultant ELF/VLF radiation of the auroral electrojet Nikolai G. Lehtinen Stanford, December 14, 2006

  2. Outline • Introduction • Kinetic equation • Comparison with Maxwellian model • Self-consistent HF propagation • DC (low frequency) conductivity • Electrojet current modulation • ELF/VLF wave generation • Open questions

  3. Generation of ELF/VLF waves

  4. HAARP High Frequency Active Auroral Research Program After upgrade in 2007: • 180 crossed dipole antennas • 3.6 MW power • ~2 GW effective radiated HF power (2.8-10 MHz) (lightning has ~20 GW isotropic ERP)

  5. HAARP and other HF heating facilities

  6. Important electron-molecule interaction concept: Dynamic friction force N2 vib. barrier Inelastic processes: • Rotational • Vibrational • Electronic level excitations • Dissociative losses • Ionization (E/N)br=130 Td where 1 Td = 10-21 V-m2

  7. Outline • Introduction • Kinetic equation • Comparison with Maxwellian model • Self-consistent HF propagation • DC (low frequency) conductivity • Electrojet current modulation • ELF/VLF wave generation • Open questions

  8. Time-dependent solution for - almost isotropic, time dependence is slow compared to w Physical processes inluded in ELENDIF: Quasistatic electric field Elastic scattering on neutrals and ions Inelastic and superelastic scattering Electron-electron collisions Attachment and ionization Photon-electron processes External source of electrons New: Non-static (harmonic) electric field Geomagnetic field Kinetic Equation Solver(modified ELENDIF)

  9. Importance of these processes • The quasistatic approximation used by ELENDIF requires nm>>w • Geomagnetic field is also important: wH~2p x 1 MHz wH wHAARP

  10. Boltzmann equation • + ordinary; - extraordinary • includes inelastic collisions • By inspection of D we see that the effect of E is reduced at high frequencies

  11. Analytical solution No inalastic collisions, mean free path l=v/nm=(Nsm)-1=const • Margenau distribution • Druyvesteyn distribution w=0

  12. Calculated electron distributions Electron distributions for various RMS E/N (in Td). f>0 corresponds to extaordinary wave (fH=1 MHz, h=91 km) • Effective electric field is smaller than in DC case: + ordinary - extraordinary

  13. Breakdown field(used for the estimate of nm,eff) h = 91 km, extraordinary, fH=1 MHz • Breakdown occurs when nion>natt • The point of breakdown (shown with ) shifts up in oscillating field • f(v) at ionization energy (~15 eV) is most important

  14. Outline • Introduction • Kinetic equation • Comparison with Maxwellian model • Self-consistent HF propagation • DC (low frequency) conductivity • Electrojet current modulation • ELF/VLF wave generation • Open questions

  15. Atmosphere heating: Maxwellian vs non-Maxwellian • Steady-state heating by HF wave produces different effective temperatures for different electron distributions • HF and DC conductivity are both dependent on electron distribution (shown DC conductivity)

  16. Outline • Introduction • Kinetic equation • Comparison with Maxwellian model • Self-consistent HF propagation • DC (low frequency) conductivity • Electrojet current modulation • ELF/VLF wave generation • Open questions

  17. HF wave propagation • Power flux (1D), including losses: • HF conductivity (ordinary/extaordinary) • n(e) is calculated from Boltzmann equation, with rms E field

  18. Calculated steady-state HF electric field • Normalized field, E/Ebr is shown • For comparison, we show the dynamic friction function • The N2 vibrational threshold or breakdown field are not exceeded for current or upgraded HAARP power

  19. Is breakdown achievable at all? Propagation with no absorption • The electric field can be higher in a non-steady state case • Electric breakdown field with altitude: • Decreases due to thinning atmosphere • But, increases due to oscillations and magnetization.

  20. Heating dynamics: Time scales of various processes • Black: energy losses to molecules and ions • Blue: electron-electron collisions (maxwellize the distribution, but do not change Teff) • Red: E-field (example for upgraded HAARP)

  21. Dynamics of self-absorption • 1 kHz square-modulated wave • Electric field is not constant during the heating half-cycle

  22. Steady-state modulated E field • The peak E/Ebr in steady-state can be several times lower than initially (at the same HAARP power) due to established self-absorption

  23. Effective electron temperature • For the generation of DJ, the difference between “heated” and “cooled” states is important

  24. Outline • Introduction • Kinetic equation • Comparison with Maxwellian model • Self-consistent HF propagation • DC (low frequency) conductivity • Electrojet current modulation • ELF/VLF wave generation • Open questions

  25. Conductivity tensor (DC) • Conductivity changes due to modification of electron distribution • Approximate formulas were used previously • Pedersen (transverse) • Hall (off-diagonal) • Parallel

  26. Steady heating conductivity modification • Pedersen conductivity is increased • Parallel conductivity is decreased

  27. Saturation of conductivity change • Conductivity change ~ input power at small power levels • When the change is a big fraction, the dependence is no longer linear • Ne=const (no ionization/chemical modification effects)

  28. Another source of nonlinearity: self-absorption f=3 MHz, x-mode f=7 MHz, x-mode

  29. Time dynamics of conductivity changes • Time scales to change the steady-state determined by energy exchange between electrons and neutrals (ions)

  30. Outline • Introduction • Kinetic equation • Comparison with Maxwellian model • Self-consistent HF propagation • DC (low frequency) conductivity • Electrojet current modulation • ELF/VLF wave generation • Open questions

  31. Electric current calculations • We assume static current, i.e. • This is justified because the conductivity time scale s/e0 >> f • Vertical B (z axis) • Ambient E = 25 mV/m is along x axis • 3D calculations

  32. Conductivity time scales(for justification of steady state)

  33. 3D stationary DJ:vertical profile Pedersen current Hall current

  34. 3D stationary DJ:horizontal slices • Vertical B (z axis) • Ambient E = 25 mV/m is along x axis Hall current (80 km) Pedersen current (90 km)

  35. 3D stationary DJ:vertical slices Hall currents Pedersen currents • Closing vertical currents

  36. Outline • Introduction • Kinetic equation • Comparison with Maxwellian model • Self-consistent HF propagation • DC (low frequency) conductivity • Electrojet current modulation • ELF/VLF wave generation • Open questions

  37. ELF/VLF radiation • Use Tim Chevalier’s FDFD code -- in future • Now: application of mode theory (stratified medium): • Ex, Ey are continuous at each boundary between horizontal layers • Change in Hx, Hy is proportional to horizontal current • Boundary conditions: Ex,y=0 at h=0, radiation at hmax • The source current is represented as a linear combination of its horizontal Fourier components • Current limitation: no Jz, but it is located higher in ionosphere and should not affect at least the Earth-ionosphere waveguide results.

  38. f=1 kHz radiation:into Earth-ionosphere waveguide • Only QTEM mode => no nulls

  39. f=1 kHz radiation:into ionosphere • We can calculate radiation of the whistler mode into ionosphere

  40. f=3 kHz radiation:into Earth-ionosphere waveguide • QTEM mode (l=105 km) and QTE1 mode (l=120 km) => nulls

  41. f=3 kHz radiation:into ionosphere

  42. Outline • Introduction • Kinetic equation • Comparison with Maxwellian model • Self-consistent HF propagation • DC (low frequency) conductivity • Electrojet current modification • ELF/VLF wave generation • Open questions

  43. Open questions • Contribution of different energy loss mechanisms • Ionosphere chemistry modification by heating • Non-vertical propagation and B • Formation of ducts by electron diffusion from the heated region • …

  44. Losses to excitation of N2 and O2 rotation • Are important at lower HF levels

  45. Long-time-scale heating effects • Ionosphere chemistry model [Lehtinen and Inan, 2006]: • 5 species • Dynamics on t > or ~1 s scale • The red coefficients depend on electron energy distribution

  46. Dependence of 3-body electron attachment rate b on Te • Can use non-thermal electron distribution (cross-section is known as a function of energy)

  47. Non-vertical propagation and ray divergence • Ray tracing for HF propagation Effect on HF heating: beam spreading

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