Solar Wind Core Electrons Maxwellian or Kappa?

Recap: Solar Wind Electron Distributions

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)

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

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

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.

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

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

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

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

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

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!

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?

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?)

{ 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.

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.

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

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. ????

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?