1. « Chocs sans collisions : étude d’objet astrophysique par les satellites Cluster » Vladimir Krasnoselskikh + équipe Plasma Spatial LPCE / CNRS-University of Orleans, and Cluster colleagues S. Bale, M. Balikhin, P. Decreau, T. Horbury, H. Kucharek, V. Lobzin, M. Dunlop, M. Scholer, S. Schwartz, S. Walker and others

2. Collisionless shocks : new results from Cluster Plan 1.Shocks in space plasmas and in astrophysics 2.Opened questions in shock physics 3.Simulations and theory 4.Multi-point measurements, what can they add to single satellite studies in space: Cluster mission 5.Small scale structure of the electric fields 6.Problem of stationarity 7.Problem of particle acceleration.

3. Collisionless shocks: new results from Cluster Supernova remnant in Magellan cloude

5. Collisionless shocks : new results from Cluster Earth’s bow shock Tsurutani and Rodriguez, 1981

6. MHD BLAST WAVES FROM POINT AND CYLINDRICAL SOURCES: COMPARISON WITH OBSERVATIONS OF EIT WAVES AND DIMMINGS

9. Collisionless shocks : new results from Cluster From Giacalone et al.,

12. Collisionless shocks : new results from Cluster Quasiperpendicular shock ThermalisationVariabilityParticle Acceleration scales electrostatic potential ion reflection species Partition fine structure structure (ripples ?) Response to upstream conditions non- stationarity ion acceleration electron acceleration

13. Notion de 2 nombre de Mach critique 1985: Krasnoselskikh, Nonlinear motions of a plasma across a magnetic field, Sov. Phys. JETP 1986: Arefiev, Krasnoselskikh, Balikhin, Gedalin, Lominadze, Influence of reflected ions on the structure of quasi-perpendicular collisionless shock waves, Proceesings of the Jiunt Varenna-Abastumani International School-Workshop on Plasma Astrophysics, ESA SP-251 1988: Galeev, Krasnoselskikh, Lobzin, Sov. J. of Plasma Physics 2002: Krasnoselskikh, Lembege, Savoini, Lobzin, Physics of Plasmas

15. Second critical Mach number

16. Conséquences: Pour les nombres de Mach « avant critiques » apparition des structures de petites échelles Variation des amplitudes des élements de la structure : « overshoot », « downshoot » et cetera Apparition des multiples « fronts» Différence de la structure vus par différents satellites

17. Courtesy of Manfred Scholer

20.  Velocity of a planar boundary (normal vector n) from individual SC times and positions at the crossings (r a – r 4 ) n = V (t a - t 4 ) Analysis methods for Multi-Spacecraft data G.Pashman and P. Daly, Eds. 24 / 08 / 01 nn 7/23 ‘four points’ derived vectors (1)

21.  Spatial gradient of density Least square estimation, from the four positions r  and the four density values n a at a given time ‘four points’ derived vectors (2) 24 / 08 / 01 nn 7/23

22. Shock questions Reformation Variability Details of the shock transition How do scales of parts of the shock vary with shock parameters (Mach number,  BN, etc)? Which parts of the shock transition are variable? Cluster: Timings  shock orientation and speed Multiple encounters with same shock  average profile, variability

23. Small scale electric field structures Data Sources Electric field from EFW –Sampling 25 Hz –2 components in the spin plane Magnetic field from FGM –Resolution 5s -1 –Timing normals Density from WHISPER

24. Small scale electric field structure Normal Incidence Frame Shock frame moves with a velocity V NIF in the plane tangential to the shock such that the upstream flow is directed along the shock normal Walker et al., 2005

25. V sh =115kms -1 n=(0.96, -0.23, 0.13)θ Bn ~77 degMa~2.8

26. V sh =49kms -1 n=(0.94, -0.17, 0.29)θ Bn ~77 deg

28. Scale size of spike-like features Walker et al., 2005

29. Scale size V Ma Walker et al., 2005

30. ΔE V θ Bn Walker et al., 2005

31. Problem of Stationarity

32. Horbury et al., 2001

33. A typical shock Select several shocks Must have similar profiles at all four spacecraft No nearby solar wind features Feb-May 2001 600 km separations 33 shocks in set Horbury et al. 2001

34. Averaging the profile Synchronise at four spacecraft  normal, speed Plot in shock coordinates Some variability between spacecraft, but large scale structure similar M A ~3.9  BN ~87º M crit1 =4.3; M crit2 =6.1 Horbury et al., 2001

36. Enhancement of |B| |B| for shock, at peak and downstream, relative to upstream value Dependence of peak value on M A Up Down Undershoot Peak Courtesy of Tim Horbury

37. Shock overshoot and undershoot How big are the overshoot and undershoot amplitudes? Plotted relative to downstream |B| Uses average profile Up Down Undershoot Peak Courtesy of Tim Horbury

38. Shock ramp scale M A ~1.9  BN ~88º Average ramp profile often well described by exponential rise Fit  scale of ramp Note: fitted “scale” is not total size of shock 6 of 33 shocks do not have “good” ramps Courtesy of Tim Horbury

39. Shock ramp scale Ramp scale increases with M A and with less perpendicular shocks Note: absolute values uncertain Courtesy of Tim Horbury

40. Regions of variability M A ~3.2  BN ~75º Critical M A ~ 1.7, 2.4 Measurements up to 18s apart Variability in foot amplitude, peak waves Different undershoot scale Courtesy of Tim Horbury

41. Variability of the shock ramp Cross-correlate profiles through shock ramp Poor statistics Significant: normal- perpendicular field components decorrelate with time, not space: waves? Field magnitude does not significantly decorrelate on these time and space scales Courtesy of Tim Horbury

42. Variability of the peak |B| Peak |B| for each spacecraft, relative to peak |B| in averaged profile Higher variability at larger M A Evidence of reformation Up Down Undershoot Peak Courtesy of Tim Horbury

43. Summary for problem of non-stationarity Measurements at 600 km separations Four profiles  “average” shock profile Variability of overshoot and undershoot amplitudes Exponential ramp, scale ~c/  pi, increases with Mach number Variability of peak |B|, higher with higher Mach number Evidence for temporal, rather than spatial, variability of shock front Future: Compilation of shock list (CIS/FGM/EFW/WHISPER, …)  better statistics Variability of parts of the shock Courtesy of Tim Horbury

45. Courtesy of Steve Schwartz

48. Problem of energetic particles acceleration

49. Collisionless shocks: new results from Cluster (from Kis et al., 2004) N(cm -3 ) 0.02 0.01 0 20 0 -20 B (nT) 0 -400 -800 V sw (km/sec) Bx,By,BzBx,By,Bz 18 February 2003 12 14 16 18 20 22

50. Collisionless shocks:new results from Cluster Energetic particles (from Kis et al., 2004) 24-32 keV 10 -1 10 -2 10 -3 10 -4 0 2 4 6 8 10 energetic particles density (cm -3 ) Distance from the shock (R E )

51. Collisionless shocks: new results from Cluster from Kis et al., 2004 0 10 20 30 40 Energy (keV) E-folding distance (R e ) 4321043210

53. Double/Triple peaked spectra - Corresponding spectra often show two Langmuir peaks of comparable amplitude and sometimes (if instrumental constraints allow) a weaker low frequency wave. - The frequencies of this triplet often satisfy the resonance condition f LF = f HF1 + f HF2

57. Electron differential energy flux versus energy and pitch angle and the corresponding electric field spectra (a) near the forward edge of the electron foreshock, at 07:04:29-07:04:33 UT, and (b) deeper, at 07:05:13-07:05:17 UT.

58. Instability of electron cyclotron waves due to loss-cone distribution of reflected/accelerated electrons.

59. Reduced distribution functions for N r /N c = 0.03 and different beam temperatures

60. Conclusions The observed loss-cone feature is always accompanied by electrostatic waves with frequencies well below the local plasma frequency. The downshifted oscillations can result from a loss-cone instability of electron cyclotron or electron-sound modes rather than a beam instability of the Langmuir and/or beam modes.