Nikolai G. Lehtinen Stanford University December 13, 2007

1. Theory: new models and results:1. Non-Maxwellian model of ionospheric heating by HF radiation 2. VLF/ELF emission by modulated electrojet current Nikolai G. Lehtinen Stanford University December 13, 2007

2. Non-Maxwellian model of ionospheric heating by HF radiation

3. HF heating of ionosphere and ELF/VLF radiation

4. HF heating facilities

5. 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

6. 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)

7. 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

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

9. 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

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

11. Electric field at current HAARP level (f=3.1MHz, x-mode) • Electric field decreases due to self-absorption no absorpsion

12. Maxwellian model • Electron distribution has a fixed shape determined by a single parameter T: • From kinetic equation, obtain time dependence of <e>=3T/2:

13. Effective temperature • Current HAARP power is high enough for the changes to be both nonlinear and non-Maxwellian (results for f=3.1MHz, x-mode) current power level Linear (DT ~ E2)

14. Conductivity changes Dashed lines correspond to Maxwellian distribution Linear (Ds ~ E2) current power level

15. Electron distribution modified by HAARP, with E=.5 V/m • Clearly seen the effect of N2 vibrational barrier

16. Square-modulated heating • Absolute change and harmonic contents of conductivity depends on non-thermal effects at current HAARP power level

17. Square-modulated heating (2) • The effect is higher if the power is increased

18. DC Conductivity tensor • Conductivity changes due to modification of electron distribution • Pedersen (transverse) • Hall (off-diagonal) • Parallel

19. Electrojet current modulation 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

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

21. 3D stationary DJ:vertical profile Pedersen current Hall current

22. 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)

23. 3D stationary DJ:vertical slices Hall currents Pedersen currents • Closing vertical currents

24. 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 • …

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

26. Long-time-scale heating effects • Ionosphere chemistry model [Lehtinen and Inan, 2007]: • 5 species • Dynamics on t > or ~1 s scale • The red coefficients depend on electron energy distribution

27. 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)

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

29. VLF/ELF emission by modulated electrojet current

30. VLF/ELF emission and propagation model • Uses mode theory to solve Maxwell’s equations in stratified medium, implemented in MATLAB • Capabilities: • Full wave 3D solution of both whistler waves launched into ionosphere and VLF waves launched into Earth-ionosphere waveguide • Magnetized plasma with arbitrary direction of geomagnetic field • Arbitrary configuration of harmonically varying currents • Both ionosphere and Earth-ionosphere waveguide • Stable against the “swamping” instability by evanescent waves • Runs much faster than FDFD and FDTD models: • Cell size can be larger than the wavelength • Vertical cell size can be variable • Can be extended to satellite altitudes

31. Method description • Find kz, E and H for all modes in each layer for each fixed horizontal wave vector k^ • Use continuity of E^ and H^ between layers to recursively find reflection coefficients and mode amplitudes, using Nygren’s [1982] order of recursion • Represent source currents as thin sheets and introduce new boundary conditions at these sheets to find fields due to sources • Inverse Fourier transform from k^ to r^

32. 1. Find the modes • Solve uniform Maxwell’s equations for nz, E, H (for ~e-iwt) • u, d are downward and upward propagating (or evanescent) modes, Im(nz) > 0

33. 2. Find refraction coefficients and mode amplitudes • Above sources d=Ruu • Below sources u=Rdd • Use continuity of E^ and H^ between layers to find recursively Ruk+1Ruk and RdkRdk+1 with RuM=0 and Rd1=-I ukuk+1 and dk+1dk with initial values specified by sources This order of recursion provides stability against “swamping” by evanescent waves and was suggested by Nygren [Planet. Space Sci., 30(4), p. 427, 1982]

34. 3. Include sources • Boundary conditions for a sheet current J=Id(z): • Find Du, Dd using the mode structure matrix F • Find u immediately above the sheet and d below the sheet using known reflection coefficients, d+Dd=Ruu, u-Du=Rdd

35. 4. “Reassemble” Fourier components • Obtain E, H from u,d • Inverse Fourier transform from k^ to r^

36. Application: Emission of ELF waves by HF-heated modulated electrojet • Modulation frequency=1875 Hz • Emission is caused by the change in electrojet current caused by HF heating • The current structure was calculated by Payne et al [GRL, 34, L23101, 2007]. It has a horizontal pancake shape • We use our method to find E and B fields

37. Collimated whistler beamWave in Earth-ionosphere waveguide

38. Why is the beam collimated? • The beam changes its shape, but insignificantly due to a large size of the emitting region (small perpendicular k-vector)

39. Poynting vector at satellite altitude (h=700 km)

40. Simulation of a satellite pass • non-zero displacement (target parameter) from the maximum of the emission

41. Field on the ground • The observed field on the ground is due to both near field and propagating Earth-ionosphere waveguide modes.

42. Summary • We developed a stable method of calculations of fields in stratified media • ELF emission by the HF-heated spot creates a collimated upward whistler beam • Calculated emitted energy is ~3 W into magnetosphere, ~1 W into Earth-ionosphere waveguide, for fmod=1875 Hz

43. Efficiency of emission as a function of modulation frequency • Because of the resonance in the Earth-ionosphere waveguide, some frequencies are more efficient

44. Understanding the energy flow from the electrojet “antenna” • The Earth-ionosphere waveguide mode “leaks” into ionosphere

45. Energy flow without reflection from Earth • The surface wave “leaks” into ionosphere

46. Origin of “lobes” of the collimated beam • The lobes are due to both surface wave and reflection from the Earth

47. In a uniform plasma, there is no sideways emission at all • This is due to collimation of the whistler beam

48. Perspective uses of the new full-wave model, for HAARP • Calculation of long-distance VLF wave propagation from HAARP • Calculation of whistler penetration into Earth-ionosphere waveguide at the conjugate point

49. Long-distance propagation

50. Long-distance propagation • We can represent the boundary conditions for an incoming wave as a vertical sheet with surface electric (J) and magnetic (M) currents: • Requires introduction of magnetic currents. For M=Kd(z) the new boundary conditions become: