1. Recent progress in our understanding of E region irregularities
Jean-Pierre St-Maurice
ISAS, U of Saskatchewan

2. Farley-Buneman waves in the E region
Basic properties and their theoretical explanation
First nonlinear complications: how to explain basic radar spectral signatures with “simple” nonlinear effects
More complicated properties related to electron heating and large aspect angle observations: nonlocal theory to the rescue
Exceptions to the rule: fast and slow narrow spectra. Not too turbulent, yet took decades to figure out!

3. 1. Basic E region irregularities properties a. Observations

4. Electrostatic Irregularities are seen between 90 and 120 km and depend on the E field

5. Low power “coherent” radars show that the most powerful echoes by far come from structures elongated along the geomagnetic field (“Field-Aligned-Irregualities, or FAI)

6. 1. Basic E region irregularities properties b. Theoretical explanation

7. What happens to the plasma below 120 km
The electrons are magnetized down to 80 km altitude and therefore ExB drift when an E field is present
The ion collision frequency rapidly exceeds their cyclotron frequency as the altitude becomes lower than 120 km.
Result: strong Hall currents, i.e. strong relative drifts between ions and electrons if the ExB drift is large
If the relative drifts are strong enough, a “Farley-Buneman” instability is excited.

8. STEP 1: quick polarization of elongated field aligned structures in the E region

9. STEP 2: The long time scale evolution includes diffusion and ion inertia (anti-diffusion in a sense)
The ions from the background arrive a bit late. This enhances the perturbed E field since all electrons are always ExB drifting.
ExB
Note: Diffusion has a stabilizing influence, as usual. +

10. 2. Trouble in paradise: Linear instability theory does well for the prediction of echo occurrence and their location but is lousy at explaining the most basic properties of observed radar spectra

11. Black: type 1, going at the ion-acoustic speed (frequent)
Cartoon of the types of spectra found in the E region
Black: type 1, going at the ion-acoustic speed (frequent)
Red: type 2, with small drift and spectral width = ion-acoustic speed (frequent)
Blue: Type 3, very narrow and much less than ion–acoustic speed (rare)
Green: Type 4, very narrow and much faster than ion-acoustic speed (rare)

12. Explanations for the basic puzzles
If we do a pure plane wave decomposition (Fourier analysis) we assume that the structures have an infinite elongation along E.
In reality we have highly elongated structures (plane wave like) but with edges. Once the edges are accounted for we have to accept that
There is decay near the edges and the decay is controlled by diffusion, meaning that the spectral width will be of the order of the ion-acoustic speed
If one sticks with Fourier analysis (plane wave decomposition) the edges are showing up through mode-coupling.
Density gradients in the elongated direction produce secondary E fields that lead to a decrease in the total field inside a structure:
Therefore as the density of a structure increases, its growth goes down.

13. Substructures must exist along wave fronts.
Plane waves break up into substructures along crests or troughs. Note that mode-coupling (Sato, 1973) and blob evolution (St-Maurice and Hamza, 2001) give identical results for E inside substructures
ASSUMPTION:
Substructures must exist along wave fronts.
A direct result of this is the formation of polarization fields that will slow their growth.

14. The structure does not rotate but its electric field does
St-Maurice and Hamza’s construct, which is very similar to Sato’s modulation along a wave front.
Illustration from Hysell and Drexler

15. Results from Sato (1972) [mode-coupling] and from St-Maurice and Hamza (2000) [elongated 2D structures]
This gives:

16. 3. Important non-local effects leading to a) Large aspect angles b) Electron heating c) Finite spectral width at Cs

17. Fourier/plane wave description
Nonlocal effects: eigenfrequency depends on altitude: aspect angle must grow and Ell with it
Fourier/plane wave description
Real space:
1- Parallel E fields
2- upward group velocity building up with time

18. Some of the mathematical steps involved
No Fourier decomposition along z
The local parallel wave number comes from the derivative of S wrt z
Plane wave decomposition kept in the plane perpendicular to B.
Conservation of wave action is obtained and describes the evolution of the amplitude in time and space

19. Implications from a monotonically increasing aspect angle with time

20. The consequences are important
Once the fast evolution in the perpendicular plane has slowed down, the increasing aspect angle makes the amplitude go down and ultimately the structures decay to oblivion. The spectral width is broadened as observed.
The parallel E fields heat the electrons (Observed). This transfers the energy of the waves back to the particles.
Large aspect angles are generated well beyond the predictions from linear theory: observed.

23. Aspect angle sensitivity at 448 MHz

24. 4. Very narrow spectra: the exceptions to the rule a) Fast narrow spectra (formerly called “type IV”)

25. Black: type 1, going at the ion-acoustic speed (frequent)
Cartoon of the types of spectra found in the E region
Black: type 1, going at the ion-acoustic speed (frequent)
Red: type 2, with small drift and spectral width = ion-acoustic speed (frequent)
Blue: Type 3, very narrow and much less than ion–acoustic speed (rare)
Green: Type 4, very narrow and much faster than ion-acoustic speed (rare)

26. Farley and Providakes, JGR, 1989.
Narrow fast echoes: 1)separate from the rest and 2) only seen with large E fields (large Te)
Farley and Providakes, JGR, 1989.

27. Narrow fast spectra: properties
Much narrower than the run-of-the-mill Cs spectra
Only seen when the electric field is very strong (in excess of 55 mV/m).
Doppler shift very close to the ExB velocity in the ExB direction
From recent interferometry results: they come from the top of the unstable layer

28. Explanation
Narrow means weak turbulence means near eigen-frequency near zero growth rate.
The eigenfrequency is actually for the ion frame of reference, i.e.,
The second term is usually neglected. BUT
At the top altitude, \Psi goes to 0 even for nonzero aspect angles. When the relative drift is just a tad above Cs we have a small growth rate and waves moving at the electron ExB drift.
CONCLUSION: the weakly growing waves end up at Cs in the ion frame, but at ExB in the absolute frame.

29. 4. Very narrow spectra: the exceptions to the rule b) Slow narrow spectra (formerly called “Type III”)

30. Black: type 1, going at the ion-acoustic speed (frequent)
Cartoon of the types of spectra found in the E region
Black: type 1, going at the ion-acoustic speed (frequent)
Red: type 2, with small drift and spectral width = ion-acoustic speed (frequent)
Blue: Type 3, very narrow and much less than ion–acoustic speed (rare)
Green: Type 4, very narrow and much faster than ion-acoustic speed (rare)

31. Narrow fast spectra: properties
Much narrower than the run-of-the-mill Cs spectra
Only seen when the electric field is very strong (in excess of 55 mV/m).
Doppler shifts around 200 m/s in spite of target velocities of 1000 m/s or more
Seen at 45 deg to the ExB direction
Recent interferometry results: they come from the bottom of the unstable layer, below 100 km altitude

32. Bivariate histogram obtained by Chau and St-Maurice (2016) at 50 MHz (4.5 m waves) during a major magnetic storm in March 2015

33. Explanation
Narrow means weak turbulence means near eigen-frequency near zero growth rate.
The eigenfrequency from 95 km altitude is strongly affected by non-isothermal electrons and collisions. It’s a complicated calculation in which
In the ExB direction the phase velocity goes up with decreasing altitudes (observed in equatorial regions)
Around 45 deg to the ExB direction the threshold velocity goes down because the electron temperature modulations from friction acts to decrease the pressure gradients (and diffusion) in the waves.
Requires relativistic precipitation to be seen: magnetic storms and south of the usual auroral region (high Kp situation).

35. Summary: E region waves
We observe elongated structures, not plane waves. This implies:
A rotation and decrease of the electric field inside the structures with the largest amplitudes coinciding with weakly growing modes moving at near the threshold speed
The edges of the structure are seen when looking perpendicular to the mean flow: the Doppler shifts are slow and diffusive decay creates spectral widths comparable to the ion –acoustic speed

36. The eigenfrequency is a function of position along the B field
The eigenfrequency is a function of position along the B field. This forces the aspect angle to grow with time, implying:
A decay of the waves after reaching a maximum amplitude near zero growth rate
The generation of an E field parallel to B, which heats the electrons and transfers wave energy to electrons
The observation of larger than expected plasma structures up to 15 degrees away from perpendicularity to B.
Fast narrow spectra come from the top of the unstable region where the growth rate is small and the Doppler shift for a ground-based observed is close to ExB .
Slow narrow spectra from from the bottom of the unstable region where the growth rate is small and the Doppler shift is way down because of collisions. Growth only happens when Te fluctuations out of phase with the density fluctuations, at 45 deg to the flow.