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« 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 ClusterQuasiperpendicular 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
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
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
Courtesy of Manfred Scholer
Courtesy of Manfred Scholer
Velocity of a planar boundary (normal vector n)
from individual SC times and positions at the crossings
(ra – r4 ) n = V (ta - t4)
Analysis methods for Multi-Spacecraft dataG.Pashman and P. Daly, Eds.
V
24 / 08 / 01
n
7/23
‘four points’ derived vectors (1)
Spatial gradient of density
Least square estimation, from the four positions rand the fourdensity values na at a given time
‘four points’ derived vectors (2)
n
24 / 08 / 01
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 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
Small scale electric field structureNormal Incidence Frame
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
Walker et al., 2005
Vsh=115kms-1 n=(0.96, -0.23, 0.13) θBn~77 deg Ma~2.8
Vsh=49kms-1 n=(0.94, -0.17, 0.29) θBn~77 deg
Scale size of spike-like features
Walker et al., 2005
Scale size V MaWalker et al., 2005
ΔE V θBn
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 2001• 600 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
• MA~3.9
BN~87º
• Mcrit1=4.3; Mcrit2=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 MA
Up
Down
UndershootPeak
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
UndershootPeak
Courtesy of Tim Horbury
Shock ramp scale
• MA~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 MA and with less perpendicular shocks
• Note: absolute values uncertain
Courtesy of Tim Horbury
Regions of variability• MA~3.2
BN~75º
• Critical MA ~ 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 MA
• Evidence of reformation
Up
Down
UndershootPeak
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
Courtesy of Steve Schwartz
Courtesy of Steve Schwartz
• Problem of energetic particles acceleration
Collisionless shocks: new results from Cluster(from Kis et al., 2004)
N(c
m-
3)
0.02
0.01
0
20
0
-20
B (
nT
)
0
-400
-800
Vsw
(km
/sec
)
Bx,By,Bz
18 February 2003
12 14 16 18 20 22
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
ener
get
ic p
arti
cles
den
sity
(cm
-
3)
Distance from the shock (RE)
Collisionless shocks: new results from Clusterfrom Kis et al., 2004
0 10 20 30 40
Energy (keV)
E-f
old
ing
dis
tan
ce (
Re)
4
3
2
1
0
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
0 7 :0 4 .5 0 7 :0 5 0 7 :0 5 .5 0 7 :0 6 0 7 :0 6 .5 0 7 :0 7
h o u r : m in (U T )
0
10
20
B, n
T
S C 3
Fre
qu
ency
, kH
z
Electron differential energy flux versus energy and pitchangle 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.
1 0 2 0 3 0 4 0f, k H z
10
10
10-4
10-5
10-6
0 10 20 30 40f, k H z
Ene
rgy
(eV
)
Ele
ctro
n en
ergy
flux
, er
g cm
-2 s
-1 e
V-1
sr
-1
Energy (eV ) Energy (eV )
log 10
( E
/ E
max
) (a) (b)
10 -2
1
10 -1
10 -3
1
10 -1
10 -2
10 -3
103
102
102
103
Instability of electron cyclotron waves due to loss-cone distribution of reflected/accelerated electrons.
0 100 200 300kV TeBe
4 9
5 0
9 9
1 0 0
1 4 9
1 5 0
1 9 9
2 0 0
- 0 . 0 8
0
- 0 . 0 8
0
- 0 . 0 8
0
- 0 . 0 8
0
Be Be
1 1.5vperp / V Tc
0
2
40 80 120 160obsB e
0.02
0.03
0.04
0.2 0.4 0.6obspcBe
g (vperp / V Tc )(a)(b)
(c)
Reduced distribution functionsfor Nr/Nc = 0.03 and different beam temperatures
1 1.1 1.2 1.3 1.4V / VTc
0.35
0.4
0.45
0.5
0.55
0.6
0.65
F
Tr / Tc = 0.1Tr / Tc = 0.01Tr / Tc = 0.001
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.
