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Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Shocks in space: Perspectives and unsolved
problems
A theoretician’s point of view
Michael Gedalin
Ben-Gurion University
Beer-Sheva, Israel
World Space Environment Forum, 2005
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Motivation and objectives
Half-century of collisionless shock research soon.
Great improvement of in situ observations.
More information on astrophysical shocks.
Great improvement of computational facilities.
Time for fully quantitative theory.
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Warnings about the talk
Theory oriented
Biased (?)
Personal views
Proper theory
Quantitative predictions.
Incomplete
A few subjects only.
Figures
For illustrative purposes only.
M. Gedalin
BEN-GURION UNIVERSITY
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Outline
1
Shock structure
Quasi-perpendicular shocks: scales, stationarity,
one-dimensionality
Quasi-parallel shocks: structure ?
2
Shock acceleration
Ion injection
Electron acceleration
3
Astrophysical shocks
4
CLUSTER role
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Quasi-perpendicular shocks: scales, stationarity, one-dimensionality
Quasi-parallel shocks: structure ?
Shock structure: low-Mach
bt
40
Monotonic transition, small
noncoplanar component.
30
20
bm
bn
10
15
10
5
0
Two-fluid HD: several
c cos θ/Mωpi
−5
15
10
5
0
−5
Ion reflection insignificant.
bl
40
30
Ion heating: downstream
gyration.
20
10
06:09:00 UT
06:10:00 UT
06:11:00 UT
From Zilbersher et al., 1998
No dissipation included.
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Quasi-perpendicular shocks: scales, stationarity, one-dimensionality
Quasi-parallel shocks: structure ?
Shock structure: high-Mach
s1347
−150
−100
−50
0
50
100
25
btotal1
20
15
Variety of profiles, fine structure.
10
5
25
Foot: ≈ 0.4Vu /Ωi , supported by
single particle equation of motion.
btotal2
20
15
10
5
−150
−100
−50
0
50
Overshoot: downstream ion
gyroradius, downstream
distribution gyration.
100
time
−10
−8
−6
−4
−2
0
2
4
6
8
10
duration1
3
2
1
Ramp: down to several c/ωpe ,
related to electron dynamics, no
theory, simulations controversial.
duration2
3
2
1
−2
0
2
4
6
8
time
10
12
14
16
18
From Newbury et al., 1998
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Quasi-perpendicular shocks: scales, stationarity, one-dimensionality
Quasi-parallel shocks: structure ?
S1D: What is this ?
MHD
1D and stationary at large scales.
Present: transition layer
Most important processes.
In situ observations at bow shock.
Timescale to compare with: ion gyroperiod
Much larger: time-independent fields for ions, shock structure
adiabatically follows slow changes of plasma parameters.
Comparable: time-dependent fields, energy non-conservation,
no pressure balance.
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Quasi-perpendicular shocks: scales, stationarity, one-dimensionality
Quasi-parallel shocks: structure ?
Shock (non)stationarity: observations
−40
−20
0
20
40
60
80
100
120
Low-Mach: stationary and
one-dimensional, combined method
(model+observations+numerical)
140
btotal1
30
High-Mach: non-stationary and/or
non-one-dimensional (Gedalin et
al., 2001).
20
10
btotal2
30
Reason: insufficient smoothing of
the downstream gyrating ion
distribution.
20
10
−20
0
20
40
60
time
80
100
120
140
From Newbury et al., 1998
No theory is available at present for
either case (what instead of
pressure balance ?).
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
scale in x for the two runs varies by a factor 2 so that in units
As can be seen from the bottom panel of Figure 3 the incident
Shock structure
of the ion scale due
to the different mass ratios
the profiles
solar wind ions interact strongly with the whistler
waves,
Shock
acceleration
Quasi-perpendicular
shocks:
scales, stationarity, one-dimensionality
both runs are comparable. Let us first discuss results from
which leads to a deceleration in the individual
whistler ofshocks
Astrophysical
structure
(upper four Quasi-parallel
panels) At t!ci =shocks:
6.7 the magnetic
field?
trains and to vortices of the incident ions in vix – x CLUSTER
phase run 1role
.
The
cross-shock
potential
increases
in
the
foot
over
20l
e
space. Since the instability results from the interaction
between the ion beam mode of the incoming solar wind has the same length scale, i.e., it extends over about 1 ion
ions and the electron whistler the reflected ions are not inertial length. As the shock reforms (t!ci = 7.3) a sharp
much affected, and these vortices do not result in individual ramp appears which leads to a large electric field spike over
"4le (not shown here), but a large part of the potential drop
small-scale reformation events.
[15] Since the instability discussed above is on the occurs already in the foot region, so that at t!ci = 7.3 only
whistler mode branch it should disappear for exact perpen- 60% of the cross-shock potential exists across the main
dicular shocks. In Figure 5 the results from high mass ratio ramp. The scale of the foot is determined by the gyroradius
two mi/me = 1840 runs with !Bn = 87! and !Bn = 90! are so that the whole potential drop occurs over a scale given by
compared. Instead comparing run 2 with the equivalent !Bn the gyroradius. The magnetic field and potential profiles of
= 90! run, we have performed two additional realistic mass the mi/me = 1840 run are similar. At t!ci = 6.4 the magnetic
ratio runs with higher Alfvén Mach number and lower field strength in the foot has increased to twice the upstream
values of the ion and electron b: run 3 with !Bn = 87!, value, and small wavelength waves are superimposed on the
MA = 6.2, be = 0.1, bi = 0.05, and run 4 with !Bn = 90! and
the same values for MA and the ion and electron b,
respectively. Figure 5 compares the magnetic field Bz profile
and the profile of the electric field Ex component between
these two runs at the same time. As can be seen from Figure
5 the short wavelength waves in the foot region indeed
disappear in the !Bn = 90! run. Furthermore, no other
electrostatic wave component is observed in the foot in the
Shock (non)stationarity: simulations
of the
ncident
s ratios
he foot
ting of
r wind
h-order
ectrons
agnetic
in the
etween
and the
rmined
ee-fluid
magnefor the
n run 2
For the
allel to
respec! to the
eglects
Early (e.g. Quest et al.,
1985): M = 22, reforming
shock, 1D full- particle.
Figure 1. (a) Stacked profiles of the magnetic field Bz
component for a shock simulation (run 1) with upstream
parameters #Bn = 87!, bi = 0.1, be = 0.2. Mass ratio is
assumed to be mi/me = 400, (wpe/!ce)2 = 10. (b) Stacked
profiles of the magnetic field Bz component for a shock
simulation (run 2) with upstream parameters #Bn = 87!, bi =
0.1, be = 0.2. Mass ratio is assumed to be mi/me = 1840,
(wpe/!ce)2 = 4.
stacked magnetic field profiles (Bz component) in the same
format as in Figure 1a for the time period 5.6– 7.3 !!1
ci . It
can be seen
that the magnetic
magnitude in the foot
From
Scholer
et al.,field
2003
increases with time, and a new shock ramp emerges out of
the foot. Thus, reformation is not an artifact of the use of an
unrealistic low ion to electron mass ratio. However, in the
realistic mass ratio case (run 2), the pronounced dip between
the newly emerging shock ramp and the former ramp
disappears. This has consequences for the identification ofM. Gedalin
Recent: M = 4.2, β = 0.1
reforming shocks.
Steepening of the ramp
down to several electron
inertial lengths
BEN-GURION UNIVERSITY
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Quasi-perpendicular shocks: scales, stationarity, one-dimensionality
Quasi-parallel shocks: structure ?
Shock (non)stationarity: theory
1200
Phys. Plasmas, Vol. 9, No. 4, April 2002
Krasnoselskikh et al.
1D theoretical model, two-fluid
HD.
Upstream whistler generation.
Shock front non-stationarity when
whistler no longer takes away the
energy and prevent steepening.
FIG. 5. The stackplot for the component B z of the magnetic field in the shock wave with # Bn !57° and M A
!5.5.
No ion reflection included.
Illustrative simulations supportive,
not definitive.
range mentioned above can be considered as nonsignifithat a self-sustained shock is formed after a transitory period
From
Krasnoselskikh
etthe use
al.,the
2002
cant
in this case.
lasting about
several ion gyroperiods calculated with
of downstream magnetic field. In the present simulations the
total run time covers about 4 ion gyroperiods calculated with
the use of upstream magnetic field.
As it was noted above, there exists a close relationship
between the properties of linear waves and the structure of
the shock waves in plasmas.1,2 In particular, the dispersion
relation influences the shape of the subcritical shock waves.
In numerical modeling, a special care should be taken to
avoid the distortion of the dispersion relation due to the
Two series of runs were performed, where the angle # Bn
between the shock normal and the magnetic field upstream of
the shock is equal to 57° and 80°, respectively, and Mach
number varies in the wide range from about 1.6 to 8.6 in the
both series. Using the simulation results, we describe the
evolution of the shock wave structure as the Mach number
increases.
We begin the analysis from the # Bn !57° shock waves.
In this case the first critical Mach number is M cr$2.54, the
M. Gedalin
Shocks in space
BEN-GURION UNIVERSITY
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Quasi-perpendicular shocks: scales, stationarity, one-dimensionality
Quasi-parallel shocks: structure ?
One-dimensionality: rippling in high-Mach
Rippling
Observations: strong variations of
normal magnetic field component.
Numerical rippling: surface waves
(?).
R. E. Lowe andMcKean
D. Burgess: Rippling inet
quasi-perpendicular
shocks
From
al., 1995
673
simulations, ripples are ion scale features at the shock front,
which move along the shock surface. The waves associated
with the rippling can be seen in the Bx component with a
wavelength of 4 to 8 ion inertial lengths and an amplitude of
around 2B0 . These peaks also appear to be connected to the
structure behind the shock, but not in any simple manner.
The ripples are most clearly visible in the shock normal component of the magnetic field, although there is
also structure due to rippling in the other field components.
Hodograms of Bx –By and Bx –Bz at the overshoot do not
show any straightforward relationship between the components, in agreement with the results of Winske and Quest
(1988).
We also ran an equivalent simulation in which the upstream magnetic field, B 0 , pointed out of the simulation
plane. In this geometry the dimensionality of the simulation
suppresses parallel propagating waves and structures, such as
AIC waves and the shock ripples, so that the shock structure
closely resembled that of a one-dimensional simulation, with
little variation in the shock normal component Bx . The average profiles of the magnetic field and density were broadly
similar in both simulations. This suggests that rippling does
not significantly affect other properties of the shock, such as
the shock width and the presence of the foot, ramp and overshoot.
Rippling: related to ion gyration,
improves pressure balance, does
not eliminate nonstationarity.
Fig. 2. A map of |Bx | taken from a simulation with θBn = 88◦
and Vin = 4vA , giving MA ≈ 5.7. The maximum value of Bx is
approximately 2B0 and the profile of |B| is superimposed.
BEN-GURION UNIVERSITY
From Lowe and Burgess, 2003
V0 . Simulation units are normalised in terms of the upstream
values of the magnetic field, B0 , the ion cyclotron frequency,
4 Fourier analysis
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Quasi-perpendicular shocks: scales, stationarity, one-dimensionality
Quasi-parallel shocks: structure ?
Structure or no structure: Patchwork
Is there any fine structure ?
Observational difficulties, no
theory.
Patchwork: steepening short
magnetic structures form the
quasi-parallel shock front. No clear
transition.
From Schwartz and Burgess, 1991
Simulated waves upstream of the
quasiparallel shock: steepen when
approaching the ”front”.
From Scholer and Kucharek, 1999
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Quasi-perpendicular shocks: scales, stationarity, one-dimensionality
Quasi-parallel shocks: structure ?
Patchwork: observations
E. A. Lucek et al.: Cluster observations of structures at quasi-parallel bow sho
A. Lucek et al.: Cluster magnetic field observations
at a quasi-parallel bow shock
1703
E. A. Lucek et al.: Cluster magnetic field observations at a quasi-parallel bowE.shock
1701
90
18:00
20:00
22:00
2 Feb. 2001, hour min (UT)
24:00
Fig. 1. Magnetic field data recorded by Cluster 4 through the quasiparallel shock on 2 February 2001. Data are displayed in the GSE
coordinate system. Panels show magnetic field elevation (θ) and
longitude (φ) angles in degrees, three magnetic field components
(Bx , By , Bz ) and the magnetic field magnitude |B| in nT.
45
0
30
−20
90
Pred θBn
20
16:00
90
20
|B|
−50
Pred θBn
0
10
0
20:00
0
20:30
21:00
21:30
22:00
22:30
20:54:30
20:54:45
20:55:00
20:55:15
2 Feb. 2001, hour min (UT)
2 Feb. 2001, hour min sec (UT)
Fig. 2. The angular variations of the spin-averaged magnetic field
Fig. 5. and
Magnetic
field
fourPanels
spacecraft
Cluster 1 (black)
upstream
at data
ACEfrom
(lightthe
blue).
showat 22 vectors/s
From Lucek et al., 2002, atmagnetic
2004
showing
magnetic
magnitude
enhancements
field
elevation
(θ) andfield
longitude
(φ) angles
in GSE within
co- a pulsation
region. field
The format
of the
figure
is asand
in the
Fig.angle
4. beordinates, magnetic
magnitude
(|B|)
in nT
tween the model bow shock normal and the magnetic field (Pred
θB n). ACE data are lagged to give good correspondence between
the magnetic field angles seen at ACE and at Cluster. When the
them
is
a
structure
less
well
correlated
between the spacedata sets do not have clear features in common, ACE data are not
craft (atbetween
20:55:00
UT).and
On21:10
these
plotted, for example,
∼20:50
UT.time scales, although the
θ°
φ°
BY (nT)
30
60
20
0
30
0
|B|
60
0
0
−30
−60
10
40
30
15
0
20
45
0
20:55:30
|B| (nT)
|B|
10
50
40
Bz
−50
0
30
0
−60
20
20
0
0
14:00
−180
|B| (nT)
30
Bz
−180
600
400
55:08
55:12
55:16
55:20
55:24
55:28
200 2 Feb. 2001, hour 20 min sec (UT)
17 06 45
17 07 00
17 07 15
17 07 30
2002 Feb 20 (051) hour min sec (UT)
0
500
|V| (kms−1)
−20
−50
180
0
−60
BZ (nT)
φ°
60
0
B (nT)
Y
φ°
By
0
|V| (kms−1)
0
0
360
−90
60
−90
0
Bx
φ°
50
50
By
0
180
−90
20
−180
|B|
0
BX (nT)
x
B
θ°
−20
180
0
180
0
NP (cm−3)
φ°
−90
0
θ°
360
0
180
20
θ°
0
90
90
90
250
17 07 45
Fig. 6. The variation of the θBn angle predicted using the bow
1. Anacross
example
a well developed
SLAM structure.
Panels
shock modelFig.
normal
theofmagnetic
field enhancement
at
magnetic
field
elevation
andelevation
longitude(θ)angles,
θ and φ (de20:55:15 UT.show
Panels
show the
magnetic
field
and longrees),in BGSE
co-ordinates,
field magniX , Bcoordinates,
Y , BZ in GSE
gitude (φ) angles
the magnetic
fieldmagnetic
magnitude
−3 ), and plasma flow
tude
|B|
(nT),
proton
number
density
N
(cm
P
(|B|) and θBn .
speed |V | (km/s). The different colours show data from the four
spacecraft: 1 (black), 2 (red), 3 (green) and 4 (magenta).
0
04 39
Fig. 2. Part o
waves and SLA
CLUSTER: quasiparallel shocks and shocklets ahead.
No correlation at 600 km separation, correlation at 100 km.
Magnetic field gradient at ion inertial length.
Support but not decisive in the absence of theory.
from the timing of the shock crossings at the four spacecraft.
Using the simplifications outlined by Horbury et al. (2002),
the model shock normal is likely to be accurate to within 10◦ ,
which is sufficient to demonstrate the trends in the magnetic
field direction across the shock on 2 February 2001. Figure 2 shows the magnetic field data from Cluster 1 (in black)
and ACE (in light blue) during the shock transition, together
with the angle between the local magnetic field direction and
the model bow shock normal (Pred θBn ) estimated using the
simplified Peredo model. Detailed comparison of the Cluster
and ACE measurements shows that throughout the interval
of interest, the delay time between ACE and Cluster is not
constant, and that there are several intervals where the correspondence is poor. In Fig. 2 the time delay is altered such
that the data sets show a good correspondence at three clear
discontinuities (at ∼20:45, ∼21:40 and ∼21:50 UT). When
the two data sets are dissimilar, such as between 20:50 and
signatures at the four spacecraft are related, there are significant differences, suggesting that spatial changes occur on
order
of the
which
at this time was
the magneticthe
field
tended
to spacecraft
rotate fromseparation,
an orientation
nearly
between
fewshock
hundred
and atothousand
kilometres.
Comparparallel to the
modelabow
normal,
a direction
more
ison
ordering
of(e.g.
the spacecraft
that although the
perpendicular
to of
thethe
shock
normal
Schwartz etshows
al., 1992;
signatures
appear
to
be
convected
towards
the
Earth (for exMann et al., 1994).
ample,
the
signature
at
Cluster
2
(red)
or
3
(green)
typically
Figure 3 shows the Cluster orbit and spacecraft tetrahedron
leads
at Cluster
4 (magenta)),
theaordering
configuration
on 2that
February
2001.
A cut though
nominalof the spacebothon
between
the leading
model bow craft
shockvaries
is shown
each panel.
At theand
endtrailing
of the edges of the
structures,
between the
two structures,
even though they
day, when the
shock isand
encountered,
Cluster
2 is separated
are three
only separated
s. 1000 km in the X–
from the other
spacecraftby
by30
about
YGSE plane, mainly
thecase
YGSECluster
direction,
lying closer
the smaller enIn theinfirst
1 (black)
sees atomuch
nose of thehancement,
magnetosphere.
The
other 2three
are
despite
Cluster
and spacecraft
Cluster 4 observing
signaquite closelytures
aligned
the orbit
in the X–Y
plane,
al-the enhanceGSEand
of awith
similar
magnitude
before
after
though separated
in
Z
,
with
spacecraft
separations
of
the
GSE 1. This suggests that the difference between
ment at Cluster
order of 400–800 km. Cluster 1 lies at the highest Z , and
M. Gedalin
Shocks in space
Between ∼
fied. The dur
scale of the tetrahedron. The timing differences between sucfor which th
cessive magnetic
field enhancements might arise from differmaximum |B
lower level of correlation, suggesting that significant variaent trajectories
the structures,
theofstructures
derestimated
tionsthough
in the plasma
occurredoronfrom
scales
100 km in this rehaving different
orientations.
analysis bein
gion. underlying
Such small-scale
processes might be related to plasma
The second
magnetic field enhancement, at 20:55:15 UT,
which can oc
thermalisation.
SLAMS. The
is more similar between the four spacecraft. Figure 6 shows
by integratin
the change2.2
in theSignatures
orientation
the magnetic
field direction,
of of
SLAMS
scale size
tal flux betw
relative to the model bow shock normal across this strucAnother
quasi-parallel
occurred
on 3 February
2002
the maximum
ture. The angle
between
the two shock
directions
is denoted
θBn .
was located
near
noon, ∼8.3
RE below the
were then plo
This figure while
showsCluster
that although
there are
differences
between
BEN-GURION UNIVERSITY
ecliptic
The region
upstream
the spaceshock
was popcraft pair per
the magnetic
field plane.
magnitude
signatures
at theoffour
ulated by exceptionally
wellfield
developed
ULF
waves, visitransverse to
craft, the behaviour
of the magnetic
direction
at the
ble most
clearly
in the
magnetic
a spatial grad
four spacecraft
is quite
similar.
Moving
fromfield
rightelevation
(upstreamand longitude anglesto(Fig.
and bythe
SLAMS,
visible asupincreases in
terest is whet
of the enhancement)
left 2),
(through
enhancement):
|B|.
When
the
tetrahedron
scale
was
∼100
km,
the
time
debetween the
stream of the leading edge, the magnetic field direction is
◦
lay
between
the
different
spacecraft
observing
an
enhancethis effect m
within 45 of the model bow shock normal; across the leadment in magnetic field magnitude was significantly shorter
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Ion injection
Electron acceleration
Injection problem
Diffusive acceleration theory
Well developed, spectra known, but: a) phenomenological (in
many cases no connection with mechanism of scattering), and b)
requires pre-acceleration (injection).
Pick-up ions
Efficiently injected: already superthermal in the shock frame.
Thermal to superthermal
Simulations show this occur but physics of the phenomenon is still
unclear.
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Ion injection
Electron acceleration
Surfing acceleration
Ions trapped by electric and
magnetic forces.
! " er / Planetary and Space Science 51 (2003) 665 – 680
V.D. Shapiro, D. Uc
u
y
+
x
B
Ey
Acceleration by motional electric
field along the front.
667
(1984) using both analytical calculations and numerics
generalized the mechanism for quasiperpendicular periodic wave with Bx !Bz and showed that acceleration in
y-direction can be signi!cantly larger than that in strictly
perpendicular case. This is possible by allowing ion acceleration in two directions. Using simulations, Lembege et
al. (1983) pointed out that the sur!ng acceleration is an
e#ective dissipation mechanism for magnetosonic wave.
Sagdeev et al. (1984) have been the !rst who considered shock sur!ng acceleration at a strictly perpendicular
magnetosonic solitary pulse and derived the resulting dissipation which transforms the pulse into a perpendicular
shock wave. Ohsawa (1985, 1986) and Ohsawa and Sakai
(1985) used simulations to investigate the formation of
self-consistent shock structure from sur!ng acceleration.
The idea of shock sur!ng acceleration has been applied
to the acceleration of solar energetic particles by fast
magnetosonic shocks in the corona (Ohsawa and Sakai,
1987), He3 ions in impulsive "ares (Ohsawa and Sakai,
1988a), energetic storm particles and ion enhancement
at interplanetary shocks (Ohsawa and Sakai, 1988b), and
cometary water-group pick-up ions at comets (Srivastava et
al., 1993). Hoshino and Shimada (Shimada and Hoshino,
2000; Hoshino and Shimada, 2002) studied electron acceleration by perpendicular magnetosonic wave. They found
that the interaction between ions re"ected by the shock
and incoming electron "ow produces Buneman instability
resulting in excitation of electron solitary structures. Electrons are re"ected by these structures and accelerate under
the action of the motional electric !eld as in the sur!ng
acceleration. They also conclude that if the shock wave
is su$ciently strong electrons undergo unlimited acceleration, since electrostatic repulsive force dominates the
Lorentz force and electrons can be trapped theoretically for
in!nitely long time. Webb et al. (1994) pointed out that
shock sur!ng acceleration may be important for interstellar
Crucial: time spent in the shock
front.
Requires low initial velocities:
pick-up only (?).
Fig. 2. Schematic diagram for shock sur!ng acceleration at a perpendicular
shock.
From Shapiro and Ucer, 2003
hancements at the interplanetary traveling shocks (Sarris
and Van Allen, 1974; Pesses et al., 1979, 1982; Decker,
1981). In the shock drift acceleration mechanism, ion energy gain is due to ion curvature and gradient drifts in the
inhomogeneous magnetic !eld at the shock front. Although
the shock sur!ng acceleration relies on a strong shock potential and shock drift acceleration does not, the most important distinction between these two mechanisms is the fact
that the shock drift acceleration energy gain is proportional
to the initial ion energy, while the !nal energy in the shock
sur!ng is greater for ions which have lower incident velocities initially (|vx0 |!u where u is the shock speed). This
happens because the particles with smaller initial |vx | are
trapped longer at the shock front, while they are accelerated
by the convective electric !eld. By this reason, shock surf-
Requires narrow transition (fine
structure helps).
Requires (?) stationarity and
one-dimensionality.
M. Gedalin
Shocks in space
BEN-GURION UNIVERSITY
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Ion injection
Electron acceleration
Surfing generalizations
Invoke additional forces for longer stay in shock
Hybrid waves against shock.
Electrostatic solitary structures ahead of the ramp.
Electrostatic potential with electromagnetic wave.
Work for electrons too ?
Require S1D or coherency - what about fluctuations/irregularities ?
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Supernova remnant shocks
High-Mach number shocks,
M ∼ 102 − 103 .
Expanding into interstellar medium
with weak magnetic field.
Radio: synchrotron from
accelerated electrons.
High efficiency of electron
heating/acceleration required.
From Chandra, NRAO
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Gamma-Ray-Burst shocks
Piston/blast unknown.
Highly relativistic shock.
Downstream ion gyroradius may exceed the system size.
Accelerated electron energies comparable with ion energies.
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
CLUSTER: capabilities vs expectations
Ability: multi-spacecraft measurements at variety of scales.
Expected: three-dimensional structure resolved.
Expected: spatial/temporal variations separated.
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Normals and (non)stationarity
2000 Dec 25 - bowshock normals
GSE positions
25
25 Dec 2000, hour 1, min sec (UT)
0
By (nT)
20
E
Y (R )
15
x
10
x20
B (nT)
20
20
10
0
0
5
10
X (RE)
20
60
15
20
25
|B| (nT)
0
−5
−5
40
Model normals
Timing normals
Coplanarity: Cluster 1
Cluster 2
Cluster 3
Cluster 4
Bz (nT)
60
5
0
40
20
5
0
30 50
31 00
E
Z (R )
30 40
0
Better shock normals.
−5
−5
0
5
10
X (RE )
15
20
25
Nonstationarity timescale estimate.
From Horbury et al., 2001
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock
acceleration
igure 4. The Ex component (in the despun satellite frame), three
components
and the magnitude of the
Astrophysical
shocks
magnetic field during the 1828 UT shock crossing by spacecraft
1. The X axis shows
time in seconds after
CLUSTER role
828 UT.
Electrostatic subshock
he asymptotic plasma bulk velocity is parallel to
etic field both in the upstream and downstream
he velocity of the HTF with respect to the NIF has
NIF
NIF
tan (qBn)| where Vup
is the
de of |V HTF| = |Vup
velocity in NIF. If qBn is close to right angle, a
ertainty in qBn results in huge errors in VHTF
ore in the cross-shock potential !HTF. Therefore
we will focus on estimating the cross-shock potential in the
NIF (!NIF). In order to estimate !NIF from experimental data
we need to take into account two terms. The first is a
projection of the electric field component along the shock
normal, spatially integrated through the shock transition
layer. The second term is the result of the satellite velocity
with respect to the NIF, i.e., Vsat-NIF = Vup! (Vup " n ) " n
Quasistationary
cross-shock electric field
spikes.
igure 5. The Ex component (red) and the magnitude of the magnitude magnetic field (blue) during the
rossing of shock at 1828 UT with an expanded time scale as observed by spacecrafts (top) 1 and
bottom) 3.
From Balikhin et al., 2002
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Summary: status
Pieces of the puzzle
Put the pieces together
Theory with predictive abilities
BEN-GURION UNIVERSITY
M. Gedalin
Shocks in space
Shock structure
Shock acceleration
Astrophysical shocks
CLUSTER role
Summary
To complete
Quasi-perpendicular shock structure (if possible at all).
Unified description of particles at shock.
To develop
Quasi-parallel shock theory.
Nonstationary shock model/theory.
Hopefully
Bridge to astrophysical shocks (or are they completely
different ?).
Breakthrough from CLUSTER.
M. Gedalin
Shocks in space
BEN-GURION UNIVERSITY