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  Chocs sans collisions étude dobjet
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

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Collisionless shocks new results from Cluster

• Plan
• Shocks in space plasmas and in astrophysics
• Opened questions in shock physics
• Simulations and theory
• Multi-point measurements, what can they add to
  single satellite studies in space Cluster
  mission
• Small scale structure of the electric fields
• Problem of stationarity
• Problem of particle acceleration.

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Collisionless shocks new results from Cluster

• Supernova remnant in Magellan cloude

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Collisionless shocks new results from Cluster
Earths bow shock
Tsurutani and Rodriguez, 1981
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MHD BLAST WAVES FROM POINT AND CYLINDRICAL
SOURCES COMPARISON WITH OBSERVATIONS OF EIT
WAVES AND DIMMINGS
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Collisionless shocks new results from Cluster
From Giacalone et al.,
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Collisionless shocks new results from Cluster
Quasiperpendicular shock
Thermalisation Variability Particle Acceleration
scales
electrostatic potential
ion reflection
species
Partition
fine structure
structure (ripples ?)
Response to upstream conditions
non-stationarity
ion acceleration
electron acceleration
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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

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Second critical Mach number
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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

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Courtesy of Manfred Scholer
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Courtesy of Manfred Scholer
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Courtesy of Manfred Scholer
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four points derived vectors (1)
Analysis methods for Multi-Spacecraft
data G.Pashman and P. Daly, Eds.

• Velocity of a planar boundary (normal vector n)
• from individual SC times and positions at
  the
• crossings
• (ra r4 ) n V (ta - t4)

na
24 / 08 / 01
7/23
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four points derived vectors (2)

• Spatial gradient of density
• Least square estimation, from
• the four positions ra,and the four
• density values na at a given time

na
24 / 08 / 01
7/23
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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

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Small scale electric field structuresData 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

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Small scale electric field structureNormal
Incidence Frame
Walker et al., 2005
Shock frame moves with a velocity VNIF in the
plane tangential to the shock such that the
upstream flow is directed along the shock normal
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Vsh115kms-1
n(0.96, -0.23, 0.13)
?Bn77 deg
Ma2.8
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Scale size of spike-like features
Walker et al., 2005
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Scale size V Ma
Walker et al., 2005
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?E V ?Bn
Walker et al., 2005
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• Problem of Stationarity

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Horbury et al., 2001
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A typical shock
Horbury et al. 2001

• 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

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Averaging the profile
Horbury et al., 2001

• Synchronise at four spacecraft ? normal, speed
• Plot in shock coordinates
• Some variability between spacecraft, but large
  scale structure similar
• MA3.9
• ?BN87º
• Mcrit14.3 Mcrit26.1

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Enhancement of B
Courtesy of Tim Horbury

• B for shock, at peak and downstream, relative
  to upstream value
• Dependence of peak value on MA

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Shock overshoot and undershoot
Courtesy of Tim Horbury

• How big are the overshoot and undershoot
  amplitudes?
• Plotted relative to downstream B
• Uses average profile

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Shock ramp scale
Courtesy of Tim Horbury

• MA1.9
• ?BN88º
• 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

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Shock ramp scale
Courtesy of Tim Horbury

• Ramp scale increases with MA and with less
  perpendicular shocks
• Note absolute values uncertain

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Regions of variability
Courtesy of Tim Horbury

• MA3.2
• ?BN75º
• Critical MA 1.7, 2.4
• Measurements up to 18s apart
• Variability in foot amplitude, peak waves
• Different undershoot scale

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Variability of the shock ramp
Courtesy of Tim Horbury

• 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

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Variability of the peak B
Courtesy of Tim Horbury

• Peak B for each spacecraft, relative to peak
  B in averaged profile
• Higher variability at larger MA
• Evidence of reformation

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Summary for problem of non-stationarity
Courtesy of Tim Horbury

• 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

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Courtesy of Steve Schwartz
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Courtesy of Steve Schwartz
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Courtesy of Steve Schwartz
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• Problem of energetic particles acceleration

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Collisionless shocks new results from
Cluster(from Kis et al., 2004)
Vsw (km/sec)
0 -400 -800
18 February 2003
20 0 -20
B (nT)
Bx,By,Bz
0.02 0.01 0
N(cm-3)
12 14 16 18
20 22
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Collisionless shocksnew results from Cluster
Energetic particles (from Kis et al., 2004)
Distance from the shock (RE)
10-1 10-2 10-3 10-4
energetic particles density (cm-3)
24-32 keV
0 2 4 6
8 10
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Collisionless shocks new results from
Clusterfrom Kis et al., 2004
4 3 2 1 0
E-folding distance (Re)
0 10 20
30 40
Energy (keV)
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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 fLF fHF1 fHF2

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Electron differential energy flux versus energy
and pitchangle and the corresponding electric
field spectra (a) near the forward edge of the
electron foreshock, at 070429-070433 UT, and
(b) deeper, at 070513-070517 UT.
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Instability of electron cyclotron waves due to
loss-cone distribution of reflected/accelerated
electrons.
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Reduced distribution functionsfor Nr/Nc 0.03
and different beam temperatures
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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.