1. Reconstructing the spacecraft potential of Cluster when in active control and other issues Maria Andriopoulou Klaus Torkar Rumi Nakamura Space Research Institute, Austrian Academy of Sciences, Graz, Austria Cross-Calibration Cluster Workshop Goettingen, 16 October 2014

2.  Sunlit spacecraft  potentials up to 10's of V  Ion emitters (ASPOC)  spacecraft potential control (  8V: Cluster)  More accurate electric field & low energy particle measurements (Pedersen et al. 2008)  However, spacecraft potential cannot be directly used for plasma density derivation with high resolution (Pedersen et al. 2008)  How well can it be reconstructed ? Active Spacecraft Potential Control

3. Method 1  "Method 1" uses data containing transitions between dense and tenuous plasma (several hours each)  a) potential of a spacecraft without active control (zero ion current)  b) potential of a spacecraft with active control  c) ion beam current  Assumption: identical plasma environment for both s/c  Method 1 result: baseline relationship between controlled and uncontrolled potentials

4.  Inward pass of Cluster on May 5, 2002 from ~20 R E to ~6 R E  C1: V sc1 < 37 V, uncontrolled  C4: V sc4 < 8 V, ~9 µA ion beam  Best fit according to method 1 and three exponential terms + comparison with Nakagawa (2000) and Cully et al (2012) formulas  Best fit spectrum for this example follows Cully for lower energies and Nakagawa for higher energies Results - Method 1

5.  Uncontrolled potential V u reconstructed from:  Fits extremely well (for several cases)  Proves method 1 is useful under given conditions:  Ion beam current ~9 µA  Electron flux dominated by low energies: secondaries negligible  Good calibration of potential measurements Results - Method 1 The controlled potential is equally useful for the derivation of electron density as the uncontrolled potential (Torkar et al. 2014) I phu (V u ) = I phc (V c ) - I aspoc

6.  Dataset: Feb 15, 2002- May 12, 2002 (Controlled  Cluster 3+4 Uncontrolled  C1)  ~100 km between spacecraft  I aspoc : 5 - 28 µA (C3 ~12-15 µA, C4 ~ 9 µA)  Even at I aspoc : 40 µA some residual variation remains  j ph consistent with previous literature, but still preliminary Results - Method 1 j ph = 85×exp(-V sc /0.92) + 7.8×exp(-V sc /4.16) + 2.4×exp(-V sc /10) j ph in [µA m -2 ] V sc in [V] Future work: further data screening, improved numerical stability, extension of the data set in time

7.  Revisit all Cluster/ASPOC data  Try reconstructing uncontrolled spacecraft potential from controlled one  Derive a global photo-electron curve in different magnetospheric regions and use this for the reconstructions  Investigate separately special cases that do not seem to fit at all the above regime  Derive plasma density and respective errors Goals

8. Initial study period: August-October 2003  Data from 27 case studies when ASPOC – on (V C4 ) in the near midnight tail (C4: ASPOC On, C1: ASPOC Off)  “Good” period to study  - all spacecraft at small distances - similar orbits to MMS - comparison with previous curves (possible Lybekk et al. 2012 in limited energy range) (Lybekk et al. 2012)  Data used for this analysis: - ASPOC (I aspoc ) - EFW (V sc1, V sc4 ) - PEACE (T e, n e )  I e - CODIF (T i, n i )  I i

9. Method 2  Calculate I e, I i and estimate photo-electron current leaving the spacecraft with ASPOC off, I phot1 (I phot1 = I e1 – I i1 )  Derive a fitting curve, using the (V sc1, I phot1 ) data of the whole interval I phot1 = f (V sc1 )  Use the curve to reconstruct the controlled V sc4 data to the expected values we would get if ASPOC was OFF I phot4 = I e4 – I i4 + I aspoc  I e4 – I i4 + I aspoc = f (V sc4 )  Derive plasma densities using this global curve (due to solar cycle, spacecraft effects, we would have to re-estimate the curve for the MMS case + different magnetospheric regions & time intervals)  Estimate accuracy of measurements

10. Results: photoelectron current  I e1 – I i1 = f (V sc1 )  Underestimation of I e1 – I i1 (ASPOC off) in low density regions  use I e4 – I i4 = f (V sc1 ) instead  2 bends in the curve (at ~9V and ~32 V) LOBE [μA]

11. Comparing with the Lybekk curve  Lybekk et al. 2012: 2003-2004 (E:10-100 eV) 8<V<13 N e =30*e (-V/3.83) [1/cm 3 ] 13<V<30 N e =3.5*e (-V/10.5) [1/cm 3 ] 30<V<50 N e =17*e (-V/6.76 ) [1/cm 3 ]  Somehow agrees well in low energies, but these are not typical of the region  Doesn’t agree if we use it for higher energies  Need to redo the fitting for our purposes (50 eV)

12. Fitting results (lobe data removed) V<9 I phot =369.2*e (-V/2.9) [μA] 9<V<32 I phot =24.9*e (-V/14.6) [μA] V>32 I phot =16.4*e (-V/16.9) [μA]  3 rd region needs revisiting  Focus on the two first regions for now I phot =369.2*e (-V/2.9) I phot =24.9*e (-V/14.6) I phot =16.4.2*e (-V/16.9)

13. Results: overplotting the controlled points to the uncontrolled ones  Our method is expected to work when:  C1 (uncontrolled SC) I ph1 = Ie –Ii (BLACK POINTS) = f(V sc1 ) C4 (controlled SC)  Ie –Ii + I aspoc (RED POINTS) = I ph4 = f(V sc4 ) = f(V sc1 ) + I aspoc  2 distinct regions for the C4 data points (RED POINTS): Region 1: following the fitted curve Region 2: below the fitted curve Region 1 Region 2

14. October 1, 2003: Crossings of Cold Dense Plasma Sheet We cannot use those points to derive a global photoelectron curve in the near midnight tail  not average conditions

15. Adding the controlled points /potential reconstruction Potential reconstruction for the whole interval Using the controlled points to construct the curve

16. Regions where reconstruction does not work  Potential variations in C4 not observed in C1 (and not related to I aspoc  Could this be related to other instrument operations (EDI)? Is there a list of operation times?  Could this be evidence of secondary electrons? I eu (V u ) = I phu (V u ) + I su (V u ) I ec (V c ) = I phc (V c ) + I sc (V c ) - I aspoc

17. Method 3  "Method 3" correlates plasma electron flux & controlled s/c potential  Goal: to cover additional effects, e.g. secondary electron production

18.  High-energy electron flux case selected to investigate secondary electron effects  Controlled potential (15 µA beam) shows 2 V peaks, unexplained by variations of plasma density  Involvement of secondary electrons ? Correlating Potential and Plasma Flux by Method 3

19.  Controlled potential 0017-0020 UT (around the highlighted peak) on 2003-08-13 fits extremely well to result of regression with electron energy flux 10 - 2000 eV using method 2  Correlation coefficients are negative 200 eV   the "normal" anticorrelation between plasma density and spacecraft potential is partially reversed  Indication of secondary electron effects Correlating Potential and Plasma Flux 2

20. Variations in potential not related to density  ASPOC ON: C3 & C4 ASPOC OFF: C1 & C2  Density profile also recoverable from V sc3/4  Low E e - visible in C4 (Attracted photoelectrons + secondaries?)  Ne_c4, Ne_c3>Ne_c1, Ne_c2 Ne ≈ N_ion of C4 density probably ok ??  Andrew  -V sc sometimes opposite to Ne  Temperature effect larger than density one?? 20

21. Variations in potential not related to density

22. C4,Codif sees low E O + ? Cold plasma or instrumental effect ? 22

23.  Electric field measurements are influenced by photo-electrons around the spacecraft  Active control re-distributes these electrons, mainly in Solar direction (E x, blue curve)  Correlation between emitted ion current (orange line) and apparent sunward component of electric field (blue line)  The modification of the sheath due to ASPOC may change the offset of the Sunward component, in this example by ~0.5 mV/m.  This is not (yet) considered in the electric field calibration Electric Field Measurements

24.  In this event, both E-field components are positively correlated with S/C potential  Electric field vector amplitude in spin plane is correlated with controlled potential Electric Field Measurements - 2

25.  In this event, mainly E y is correlated with S/C potential  Only the controlled potential is correlated with E (mainly E y ) Electric Field Measurements - 2

26. Discussion – Future work  Derive the curve considering other magnetospheric regions/time intervals and compare the results (currently working on magnetotail intervals of 2001-2002-2003-2004, but need to be careful with our data selection, also spacecraft distances will be an issue  Derive curves for different temperatures??  Assess what are our limitations for reconstructing uncontrolled spacecraft potential  Exclude data when we might have other instrumental issues..  We need well calibrated data  Understand the role/contribution of secondary electrons

27. Summary  Work on reconstructing the uncontrolled potential from the controlled one  plasma density estimation  Studied periods from February - May 2002 (for method 1) and from August – October 2003 (near-midnight tail) and ongoing work for August-October 2001-2002-2004 (method 2 and keep trying more methods..)  Many cases where reconstruction works very well, results from larger statistics  various issues need to be considered  In any case, density variations still seen in controlled spacecraft potential (however, other times we also see other (possibly temperature-relate) variations in both controlled + uncontrolled spacecraft potentials