1. Walen and Slow-mode Shock Analyses Applied to High-Speed Flows of the Near-Earth Magnetotail S. Eriksson 1, C. Mouikis 2, M. W. Dunlop 3, M. Oieroset 4, D. N. Baker 1, C. Cully 1, H. Reme 5, and A. Balogh 6 1 Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, USA 2 Space Science Center, University of New Hampshire, Durham, USA 3 Rutherford Appleton Laboratory, Chilton, UK 4 Space Sciences Laboratory, University of California, Berkeley, USA 5 Centre d’Etude Spatiale des Rayonnements, Toulouse, France 6 Imperial College, London, UK Contact information: eriksson@lasp.colorado.edu

2. Outline Introduction Introduction 1. Tail reconnection and slow-mode shocks 2. deHoffmann-Teller and Walen analyses 3. Slow-mode shock criteria Cluster observations Cluster observations 2001-08-27 from 03:50 UT to 04:35 UT 2001-09-15 from 03:55 UT to 05:20 UT 2002-08-21 from 07:50 UT to 08:40 UT Summary Summary

3. Tail Reconnection and Slow-mode Shocks [Hill, T.W., JGR, 80, 4689, 1975][Feldman et al., JGR, 92, 83, 1987] Acceleration in tail reconnection is assumed to take place across a slow-mode shock (SS) connected to the diffusion region. SS generated due to near-symmetric conditions (comparable plasma density and magnetic field strength) on either side of the current layer. Configuration essentially that of Petschek [1964] (above right).

4. Tail Reconnection and Slow-mode Shocks [Hill, T.W., JGR, 80, 4689, 1975][Feldman et al., JGR, 92, 83, 1987] Slow-mode shocks were first observed in the tail by e.g. Feldman et al. [1984, 1987] using the Rankine-Hugoniot (RH) jump conditions on ISEE 2 data. Later confirmed by Geotail RH observations [e.g. Saito et al., 1995; Seon et al., 1996] and by Wind data [Oieroset et al., 2000] using the shear-stress balance test on Wind data 60 Re downtail.

5. deHoffmann-Teller Analysis [Khrabrov and Sonnerup, ISSI Sci.rep., 1998] The existence of an HT frame indicates the presence of a quasi-stationary coherent pattern of magnetic field and plasma velocity.

6. Shear-Stress Balance (Walen) Test Disturbance generated by reconnection propagates away from the diffusion region at a field-aligned phase speed in the HT shock frame determined by the type and strength of the shock.

7. Shear-Stress Balance (Walen) Test The sign of the Walen slope depends on whether the B-field is parallel or antiparallel to the flow direction.

8. Walen Analysis in the Magnetotail Walen slope Oieroset et al., JGR, 105, 25,247, 2000.

9. Walen Analyses at Wind (x= -60 Re) Oieroset et al., JGR, 105, 25,247, 2000. (Note that there is no ion composition in the Wind data set and that these slopes were derived assuming 100% H +.) Earthward jet Negative Bx Walen slope should be positive

10. Slow-mode Shock Criteria

11. Cluster Observations on 2001-08-27 ABC

12. Walen Analyses 2001-08-27 A: Tailward flows in Northern Hemisphere

13. Walen Analyses 2001-08-27 B: Earthward flows in Northern Hemisphere

14. Walen Analyses 2001-08-27 C: Earthward flows in Northern Hemisphere

15. Shock Analysis on 2001-08-27 up1down1up2down2 PpPpPpPp0.200.240.010.03 PbPbPbPb0.180.150.090.06 theta 28 o 11 o 40 o 10 o NpNpNpNp0.280.300.020.04 TpTpTpTp4.55.12.45.6 SpSpSpSp1.051.061.201.25 MAMAMAMA0.760.800.310.33 MIMIMIMI0.860.820.400.34 M SM 1.070.851.760.50 AC ABC

16. Shock Normal Optimization 2001-08-27

17. Cluster Observations on 2001-09-15 ABC

18. Walen Analyses 2001-09-15 A: Tailward flows in Northern Hemisphere

19. Walen Analyses 2001-09-15 B: Tailward flows in Northern Hemisphere

20. Walen Analyses 2001-09-15 C: Tailward flows in Southern Hemisphere

21. Shock Analysis on 2001-09-15 up1down1up2down2 PpPpPpPp0.150.300.250.29 PbPbPbPb0.220.040.110.05 theta 71 o 42 o 57 o 36 o NpNpNpNp0.420.520.620.56 TpTpTpTp2.23.42.42.8 SpSpSpSp0.930.960.900.93 MAMAMAMA0.330.670.560.76 MIMIMIMI1.010.901.040.94 M SM 1.660.931.250.98 AB BAC

22. Cluster Observations on 2002-08-21 ABC

23. Walen Analyses 2002-08-21 A: Tailward flows in Northern Hemisphere

24. Walen Analyses 2002-08-21 B: Tailward flows in Northern Hemisphere

25. Walen Analyses 2002-08-21 C: Tailward flows in Southern Hemisphere

26. Shock Analysis on 2002-08-21 up1down1 PpPpPpPp0.140.24 PbPbPbPb0.370.13 theta 63 o 40 o NpNpNpNp0.150.19 TpTpTpTp5.07.0 SpSpSpSp1.121.14 MAMAMAMA0.370.51 MIMIMIMI0.810.67 M SM 1.630.77 B BAC

27. Summary The Walen test together with the location of Cluster suggest the presence of slow-mode shocks on the tailward sides of near-Earth X-lines (X>-19 Re) for three events: 2001-08-27, 2001-09-15, 2002-08-21. The Walen test together with the location of Cluster suggest the presence of slow-mode shocks on the tailward sides of near-Earth X-lines (X>-19 Re) for three events: 2001-08-27, 2001-09-15, 2002-08-21. Earthward jets seemingly fail the Walen test more readily than tailward jets. Earthward jets seemingly fail the Walen test more readily than tailward jets. Joint Walen and RH analyses generally confirm the presence of slow-mode shocks during accelerated tailward flows. Based on three events and several jets. Joint Walen and RH analyses generally confirm the presence of slow-mode shocks during accelerated tailward flows. Based on three events and several jets. Shock-normal analyses suggest that magnetic coplanarity theorem results in a normal near the optimized (minimum RH deviations) direction. Shock-normal analyses suggest that magnetic coplanarity theorem results in a normal near the optimized (minimum RH deviations) direction.