1. Solar Wind Core Electrons
Maxwellian or Kappa?

2. Recap: Solar Wind Electron Distributions

3. Limitations of Existing Measurements
140eV
70eV
Kappa distributions and Maxwellians look very similar at low energy.
Typically very few data points at low energies.
Velocity (104 km/s)

5. Question:
Can you better describe the solar wind core with a kappa distribution than a Maxwellian?
They look similar at low energies but, for a given set of parameters, are not exactly the same.
What is the equilibrium state of partially collisional plasmas? – It doesn’t necessarily have to be Maxwellian.
Can you do away with these really ugly multicomponent solar wind models?
Can you describe the solar wind
Haaland et al., Ann. Geophys. 2010
We need high energy resolution measurements of the electron VDF

6. More Than You Ever Wanted To Know About Cluster PEACE
You measure different energies by varying (sweeping) the potential difference between the hemispheres.
E = Electron Energy
V = interhemispheric potential difference
d = distance between hemispheres
r = radius of curvature

7. More Than You Ever Wanted To Know About Cluster PEACE
Instantaneous field of view of 180° x 5°
Each sensor covers 4π sr via the spacecraft spin.
Angular resolution of 15° in polar direction (segmented detector)
Flexible angular resolution in azimuth (spin plane) direction.

8. Tradeoff Between Energy and Azimuth Resolution
Each segment of the detector reads out 256 times per second
During this time the spacecraft spins 90 degrees
Faster Voltage sweeps = higher azimuth & lower energy resolution
Slower voltage sweeps – lower azimuth & higher energy resolutions V
Time
(accumulations) 32 64
128

9. Tradeoff Between Energy and Azimuth Resolution
Each segment of the detector reads out 256 times per second
During this time the spacecraft spins 90 degrees
Faster Voltage sweeps = higher azimuth & lower energy resolution
Slower voltage sweeps – lower azimuth & higher energy resolutions V
Time
(accumulations)
To study the spectral shape of the core, we need this one: ‘LAR Mode’
59 energies between 4eV and 1000eV
Cf. Wind 3DP public data - 15 energies between 10eV and 1000eV
Campaign of ~70 burst modes (each ~85 minutes) ‘for solar wind turbulence studies’ in this mode from 2007 – 2013
4 spacecraft * 70 intervals * 85 minutes * 15 distributions per minute = 357,000 distributions – hopefully enough! 32 64
128

10. Example Interval: 2010/04/02-03
Dawnside, just upstream of the bow shock.
Need to be careful of the foreshock.

11. Example Interval: 2010/04/02-03 Grey lines show burst mode interval.
Unfortunately none of the intervals have <v> > 500 km/s

12. Electron Distribution Functions
1000
Phase Space Density
100
Energy (eV)
Spacecraft Potential
Photoelectrons 10
23:30
00:00
00:30

13. Time Averages & A Problem: Spacecraft Potential Underestimate?
????
Still have what looks like photoelectrons below 2eV.
EFW underestimating potential by 30% or is something more interesting going on?
Spacecraft
Potential from EFW
(All electrons above this energy should be natural)
~6.5V
Here I’ve corrected for potential by subtracting 6.5 from each measured energy bin.
Bodge an additional correction for now and see what happens!

14. Applied Extra 2 Volts Correction Problem: Separating Core and Halo
Still have 9 data points < 10 eV
Usual: 2 or 3
Next problem: if you only want to fit functions to the core, how do you exclude the halo?

15. Applied Extra 2 Volts Correction Problem: Separating Core and Halo
Still have 9 data points < 10 eV
Usual: 2 or 3
Next problem: if you only want to fit functions to the core, how do you exclude the halo?
Fit over a limited energy range:
Take the point at which the power law tail takes over (30eV here)?
Just use 10eV as a hard limit?
(Is the core/halo difference just a function of low resolution measurements anyway?)

16. { Kappa Vs Maxwellian Constant The important bit
E = Electron Energy
E0 = Energy of Peak Flux
κ = kappa (spectral index)
As κ∞, the distribution becomes more Maxwellian.
κ > 10: Effectively Maxwellian
Haaland et al., Ann. Geophys. 2010
This means we can just look at how κ varies as a function of other parameters to see how Maxwellian the core is, and when.

17. Fits to the mean VDF A = 74450 E0 = 11.29 A = 73771 κ = 1.5 E0 = 9.82
κ = 2.83
In both cases a Kappa distribution fits the low energy data better than a Maxwellian with the A and E0 same parameters (No separate fit yet).
By fitting up to 30eV you can describe the rest of the distribution pretty well.
Worth continuing.

18. Next Steps Check the ion data properly:
A lot of the intervals have this during the burst mode.
Some special mode that’s bad for moments?
Data gaps?
Would be handy to estimate a velocity from the ion distributions directly if the former.
Should be easy enough to check either in the archive directly or using the CIS

19. Next Steps Spacecraft potential correction: Ways to check:
Is it actually an underestimate?
If so so, how common is it?
If not, what’s going on?
Ways to check:
Calculate moments taking into account a progressively higher spacecraft potential until the density matches that derived from the wave data.
Should give us the true potential.
Has the CSA WHISPER Density product already been cross-calibrated to the electrons?
Could also redo Cully et al., 2007 model of Cluster/plasma interactions for solar wind case, though this would probably be a paper in itself.
Ask Harri.
????

20. Next Steps Fit Maxwellians and Kappas to each electron distribution.
Use only those azimuths perpendicular to solar wind velocity vector so no frame transformation is needed.
Take into account Poisson error on the count rate -> will need to transform to/from counts per accumulation
Take into account energy bin size
This way we’ll get a proper uncertainty on the fit parameters.
See how fit parameters vary as a function of solar wind speed properties.
Hardest part: Separating Core and Halo?