« 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

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.

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

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

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

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

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

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 : Galeev, Krasnoselskikh, Lobzin, Sov. J. of Plasma Physics 2002: Krasnoselskikh, Lembege, Savoini, Lobzin, Physics of Plasmas

Second critical Mach number

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

Courtesy of Manfred Scholer

 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)

 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

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

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

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

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

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

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

Scale size V Ma Walker et al., 2005

ΔE V θ Bn Walker et al., 2005

Problem of Stationarity

Horbury et al., 2001

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

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

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

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

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

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

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

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

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

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

Courtesy of Steve Schwartz

Problem of energetic particles acceleration

Collisionless shocks: new results from Cluster (from Kis et al., 2004) N(cm -3 ) B (nT) V sw (km/sec) Bx,By,BzBx,By,Bz 18 February

Collisionless shocks:new results from Cluster Energetic particles (from Kis et al., 2004) keV energetic particles density (cm -3 ) Distance from the shock (R E )

Collisionless shocks: new results from Cluster from Kis et al., Energy (keV) E-folding distance (R e )

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

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.

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

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

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.