1. Update on the interpretation of spacecraft potential during active control Klaus Torkar IWF/OAW, Graz, Austria MSSL, October 26 th, 2006 acknowledging support from P.-A. Lindqvist, P.M.E. Décréau, I. Dandouras, A.N. Fazakerley, H. Kahn, H. Laakso, H. Jeszenszky, and the ASPOC, CIS, EFW, PEACE, and WHISPER Teams

2. Objective and Concept  Derive a method that allows to reconstruct the uncontrolled spacecraft potential (V sc ) from the residual, small variations of the controlled potential when ASPOC is turned on  Note: the estimation of density from V sc is another story. The method presented here shall only allow to use the usual formulas for density estimation from the spacecraft potential irrespective of the state of ASPOC  Find a representation V free =f(V ASPOC-ON ) which is robust against variations of plasma temperature, variations of the photoemission, and changes of the EFW bias current  The correction method ideally fulfils the following conditions:  small number of coefficients, ideally linear fitting  transformation is physically meaningful  Test the accuracy of the method for all conditions

3. Status  Initial presentation at CAA Calibration Meeting in March, 2006, and at COSPAR 2006.  Promising first results  A both reliable and practical conversion method is still to be found  Studies of various methods are ongoing  Accuracy and limitations of the finally chosen method need to be addressed

4. Change of spacecraft potential due to the ion beam (ASPOC)  Is the controlled spacecraft potential (C4) still usable as a proxy for density, and under which conditions ? ASPOC ON ASPOC OFF data show spacecraft-to-probe potential, spin-average

5. Simulation of spacecraft potential free- floating controlled  The potential controlled by a constant ion beam:  approaches a constant value at low n, independent of plasma  follows the uncontrolled potential at high density.  Curves shown are valid for 10 µA ion current on Cluster.

6. Spacecraft potential vs. density relation Spacecraft potential [V] Density [cm -3 ]  The variation of the potential following approximately was illustrated by Ishisaka et al. (2005) for Geotail. Overlay: previous model for ASPOC ON and OFF at 10, 100, and 1000 eV

7. Estimation of free floating potential from the controlled potential  The relation between controlled and uncontrolled potential is almost independent of electron temp. T e.  The correction term, f, for the potential V uncontrolled = V controlled + f(V controlled ) may be approximated over a wide range of spacecraft potentials by a simple exponential function.  Relation is still non- linear near V max (low density)  Results are less accurate in the steep part of the curve (near V max ).

8. C1 and C3, 2002-04-30  Original potential data; distance C1-C3  100 km  C1: free floating potential, C3: 12 µA ion beam

9. C1 and C3, 2002-04-30  Linear correlation C1 - C3

10. C1 and C3, 2002-04-30  Potential of C3 reconstructed by exponential fit  C1: ASPOC off, C3: 12 µA ion beam ?

11. C1, C4, 2001-04-02  C1: ASPOC OFF, C3: 12.5 µA C4: 10 µA  Potential of C4 reconstructed using coefficients from fit during this period original reconstructed  Time shift C1-C4 due to 600 km distance

12. Correlation of potentials when ASPOC ion beam is turned on  Instead of inter-spacecraft comparison, this method compares potential of one s/c over beam current changes  Plots shows all 0-12 µA transitions on Cluster 3 in 2001  Exponential correction is applicable even at high potentials

13. Discussion  Reconstruction of the free floating potential is possible, using a simple expression.  The coefficients c 1, c 2 vary with conditions.  c 1 varies mainly with the known ASPOC beam current  Would other representations provide better fits? Conditionc2c2 Range of controlled potential Theoretical model0.711... 6 V C3, summary of 20010.831... 8 V C4, summary of 20010.701... 8 V C3, 2002-04-301.194.5... 6.5 V C3, 2001-04-021.056.3... 7.6 V

14. C1 and C3, 2002-04-30  Cubic fit C1 - C3

15. C1 and C3, 2002-04-30  Potential of C3 reconstructed by cubic fit  C1: ASPOC off, C3: 12 µA ion beam ( )

16. C1 and C3, 2002-04-30  Fit (V free -V ASPOC ) as a function of (V max -V ASPOC )

17. C1 and C3, 2002-04-30  Potential of C3 reconstructed by fit to V max -V ASPOC  C1: ASPOC off, C3: 12 µA ion beam ? ( )

18. C1 and C3, 2002-04-30  Linear relation forced to match at min. and max. potential

19. C1 and C3, 2002-04-30  Potential of C3 reconstructed by linear relation enforced  C1: ASPOC off, C3: 12 µA ion beam between o o o ( )

20. Summary  The reconstruction of the free floating potential of a potential-controlled spacecraft is possible, using simple expressions  The errors are reasonably small, but there is not yet one single representation that gives optimum results in all conditions  Manual calibration may be needed for best results  Future work will aim at establishing appropriate correction terms for all periods with controlled spacecraft potential