Shock structure and ion dynamics

Shock structure and ion dynamics
Michael Gedalin1 and Michael Balikhin2
1
2
Ben-Gurion University, Beer-Sheva, Israel
ACSE, University of Sheffield, Sheffield, UK
8th Annual International Astrophysics Conference, Hawaii, 1 7 May
2009
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
1/1
Motivation and objectives
Collisionless shock is a multi-scale structure (foot, ramp, overshoot,
sub-structure in the ramp).
Kinetic effects responsible for the structures (reflection, gyration).
Implications of the structure for kinetic effects (heating, acceleration).
Warning:
Theorists view, biased
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
2/1
Outline
Evolution of views
From MHD smooth transition to fine structure
Relection-gyration
Same mechanism, temperature dependence, ion heating, collisionless
relaxation, escaping ions
Peculiar shocks
Low heating, strong acceleration (termination shock, SNR shocks)
If not stated otherwise:
Quasi-⊥, 1D, stationary
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
3/1
MHD
Discontinuity: deceleration of the flow, jump in density, magnetic
field, temperature.
RH relations.
No width, no structure.
Limits of validity.
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
4/1
Structure: Soliton-to-shock theory
Nonlinear equation for dispersive
waves (fast magnetosonic).
Allows a soliton solution for
M > 1 (large amplitude,
amplitude-velocity relation).
Non-existence of the solution for
sufficiently large amplitudes Mach numbers, beginning of ion
reflection.
Ion reflection causes dissipation
- converts soliton to shock.
From Sagdeev (1967)
Implicit kinetic effects !!!
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
5/1
ron-ion collisions are assumed to be negligible in the shock wave.
ure of the author's model is that the reflected ions have drift velocities
ctrons sufficientlylarge to generate the electron-ion drift instability,
o sweep the electrons along with them to produce a beam moving
f the sub-shock as shown in Fig. 2. We shall use the subscript "to
Foot: kinetic effects
Incident
Ion reflection - ion density, ion
current ahead of the transition.
Pre-increase of the magnetic
field ahead of the transition.
I
I
!
Only part of ions are reflected kinetic effect !!!
Early models: specular
reflection, ignoring nonzero
width and internal structure.
FIG.2.-Orbit of reflected ion in the shock frame.
From Woods (1971)
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
6/1
Reflected ion observations
From Sckopke et al. (1983)
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
7/1
”Typical shock” as of 1986
From Scudder et al. (1986)
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
8/1
We do not have plasma data for this shock, but the strong
magnetic field suggests that beta may be low.
[9] Figures 5 and 6 show another comparison pair
obtained at STEREO A on August 25, 2007, and at
STEREO B on November 9, 2007. They both have a small
upstream precursor, but have major downstream wave
structure, even though they are quasi-perpendicular shocks
with shock normal angles of 71! and 64!. The precursor
Observations up to now: low-M shocks
normal direction. The
to the downstream wav
field. Thus, the max
determined by the wav
6, the waves are domin
mainly aligned along
along the projection of
less well-determined,
Measured in the LN
on September 2, 2007
January 14, 2007; 17
November 9, 2007. Th
sional suggests that th
obtain high-resolution
3. Discussion and
L03106
RUSSELL ET AL.: WAVES AT LOW MACH NUMBER SHOCKS
L03106
Figure 5. Eight-Hertz magnetic field in shock normal
coordinates for the August 25, 2007, STEREO A shock.
Comments for the caption of Figure 1 apply. This is to be
contrasted with Figure 4.
[11] We have exam
planetary medium du
STEREO A and B out
is a very rich data set
Mach number shocks.
these shocks to test
downstream waves. Th
a range of angles to
broad range of plasm
common occurrence, b
[12] The downstream
the magnetic field pe
3 of 4
Figure 4. Eight-Hertz magnetic field in shock normal
From Farris coordinates
et al.for(1993)
the January 14, 2007, STEREO A shock. Figure 6. Eight-Hertz magnetic field in shock normal
From
Russell
al.STEREO
(2009)
coordinates for
the Novemberet
9, 2007,
B shock.
Comments for the caption of Figure 1 apply.
This is to be contrasted with Figure 6. Comments for the
caption of Figure 1 apply.
the wave is not propagating along the shock normal, but at
Gedalin and
Shock structure and ion dynamics
AIAC 8, 2009
an Balikhin
angle of 40! (See Table 1).
9/1
Observations up to now: high-M shocks
From Newbury et al. (1998)
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
10 / 1
Ion dynamics at quasi-⊥ shock front: basic physics
Simplest description: magnetic jump, potential jump, small
width.
Deceleration in the ramp by the potential - substantial,
deflection by the magnetic field - weak.
Sensitivity to the initial conditions: specular vs non-specular.
Low vT /vu - non-specular: crossing the ramp, gyration
downstream, coming back to the ramp (some), crossing again.
Gyration of transmitted ions - same mechanism.
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
11 / 1
Ion dynamics: test-particle analysis
Advantage: can study parameter
dependence independently
vvx
Disadvantage: no
self-consistency, parameter sets
may be not realized in nature
4
2
0
!2
!1
0
1
2
vvx
xx
Choose Alfvenic Mach number
M, magnetic ratio R = Bd /Bu ,
1
upstream ion βi , cross-shock
0.5
potential s = 2eϕ/mi vu2 = 0.45,
0
width ≈ c/ωpi . Trace particles.
!0.5
Calculate
Pion pressure
2
pi,xx =
mi vx for a number of
!1
!0.1
0
0.1
layers. Compare with pressure
xx
balance
From Gedalin (1996)
pi,xx + pe,xx + B 2 /8π = const.
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
12 / 1
re
foot region of the shock where the magnetic field is weaker,
the transmitted ones are prevented from doing so by the potential overshoot. This point is made clear when overlaying
the electric field profile on the phase space plots of the two
Ion
dynamics: simulations
ion subpopulations(Figure 5). This is a simplificationof a
1)
2)
lk
to
(a)
•o 'BTM
....
• ....
(b)
•''
•o •-•. . '; • :"-
eof
Shock forms by
itself
ty
in
ey
e
se
ck
ri-
.
'
Advantage:
self-consistency
.
'."'I'
.......
ß-- - Vy (R.)
',:.
ß
-
.
at
he
of
in-
ed
)of
'7,
, ß , , I ,,
- -'V;iTS' ....
. ,•,
' ....
o' "'
'•'••
'7
ms
0
nin
i ! i i i ....
lb
, , , I .
-
"'
-
•1•, , , , I , ,
i0
•0
x (c /wpi)
0
10
20
x (c /wpi)
ces •ig.
ck.
ns.
5. Ion ph•e spies w-v• and w-vu, showingtoo[ion of
•he [rans•[ed
([bird •d •[h panels from
reflec[ed-gyra[ing(secondand fo•[h panelsfrom [he lop) subpop•a•ions (a) when •hey •rs• enco•er •he shock
Disadvantage:
parameters
inter-related,
difficult to
separate different
effects
he some la•er lime. The magnetic field is shown for reference, •d
gin [he •! profile (solid•rve) has been orerich on [he •-,•plo•s.
From Gedalin
Burgess
et al. (1989)
and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
13 / 1
Gyration and reflection: theory and simulations
M. Balikhin rt al.
(S/9)254
“ramp”
“foot”
“overshoot”
downstream
upstream
30
I
I
OO
1250
bLI
vx _;:m
m/sac)
VY
(1
600
0
vx
-600,
vY
FzQ
1250
x (km)
Figure
4:
2500
x (km)
2500
-be-
0
2500
x (km)
A typical profile of a supercritical quasiperpendicular shock. From /21/.
From Burgess et al. (1989)
eral theory of resistive-dispersive transition, described above. Fanis et al/19/in their study of low /3 shocks
also put great attention to the subcritical shocks. They confirmed previous result that wavelength of wave
From Zilbersher et al. (1998) and
precursors is wavelength of standing whistler waves. Fanis et al /19/ also noted that ramp width is larger
then half of the wavelength of precursor, as it should be if the ramp was just a part of the largest whistler
Gedalin et al. (2000)
wave cycle. It is necessary to note here, that the dispersion relation is valid only for the waves of infinitely
small amplitude. So this approach cannot be accepted in the study of ramp itself, where change of magnetic
Gedalin and Balikhin
Shock
and
dynamics
fieldstructure
is of the order
of ion
the magnetic
field itself.
AIAC 8, 2009
14 / 1
underlyingphasespacedistributionis a (convectedbi-)
Maxwellian. Near the bow shock,the ion distributions are
far from this state, both upstream in the shockfoot and
also somedistance downstream, as has been demonstrated
in the past, for example in S83. However, that study was
based on ISEE two-dimensionaldata and dependedon the
THERMALIZATION
AT COLLISIONLESS SHOCKS
magneticfield to be suitably orientedif, for example, gyrophase information was to be obtained. Here, arbitrary
cutsregion.
can be
made
profiles and for the extensiveovershoot
This
tight through any of the three-dimensional
Gyration and reflection: downstream ion heating
788
BURGESS ET AL.:
•
Total
.........
Reflected
.............
Transmitted
to.[.-'N' ' ' ' ....
' ....
ION
' ' '-.]
'*t
a
ß
.
distributions
that are transmitted.
correspondencebetween the transmitted
and total density
profilesis clearly visiblein Figure 6a, which
shows
the denFigure
3 shows
two suchdistributionseachof which is
sities of the two subpopulations.The double-humpedstrucrepresentedby three mutually orthogonaltwo-dimensional
ture had previouslybeen attributed to a displaced"turningpoint of the gyrating stream" relative to the positionwhere
the incomingions"pileup" [Leroyet al., 1982,p. 5085].
Perhaps the most striking feature of Figure 6a is the
large reflected-gyratingion densityin the foot, which can
be larger than the transmitted ion density. This is an in-
ß•'-.
.
.•
i
....
o,!- 'V• ' ' ' ....
I
.
, ß '-
c
,.
o , :.:,_,,"
,::,,,,,,:.... ß
.•.
I
....
ß
I
'-.-'
'
'
I
I
ß
ß
....
I
ß
ß
I
....
I
'
'1
d 1
,
,
ions are reflected at the shock.
Other
x (c / wpi)
f reflected-gyrating and transmitted contributions; the discrely
Gedalin and Balikhin
dence. Th
which sug
specular-
In the fo
of ion distr
numerical
sametype
studieshavefoundsimilarratios[e.g.,Leeet al., 1987],and
the small discrepancies
in the exact valueare most probably
due to the use of different plasma parameters and different
simulation schemes. By contrast, the density ratio of the
two subpopulations is not constant, but changesquite considerably along the box. Notice also that the large increases
seen in the bulk density profile are almost entirely due to
correspondingincreasesin the density of the transmitted
ions, a result of the gyrational motion of this population, as
discussedabove. This is in contrast to previous interpretaFig. 3.
downstreamion phasespacedistributions
tions which attribute the compressions
and Three-dimensional
rarefactions in
by three
orthogonal two-dimensionalcuts. Distribution
the densityand magneticfieldto therepresented
gyratingstream
[Leroy
a was measuredat 0656:45 UT, that is, near shock 3i, and the lower
et al., 1982].
one, b, near the centerof the magnetosheath
interval,at 0705:08UT;
seealsothe tick markson the B(t) profilein the box at the lower
Heating
right. The cuts are oriented as follows: cut 1 contains the GSE z
Figure 6d shows the profiles of the
kinetic
temperature
axis (horizontal)and the magneticfield vector B; v indicatesthe
perpendicularto the magneticfieldprojected
(Tx = 1/2(T•
+ Tyy))
direction
of the plasma bulk flow vb. Cut 2 is plane 1
of the two subpopulations and the total perpendicular temrotated by 90ø about B and offsetfrom the origin by vbx; the E axis
perature profile. The main features are
closely
related
to the of -v b x B. Cut 3 is perpendicular to B
indicates the projection
details of the motion of the ions. Entering the foot of the
andpasses
through
vb (i.e.,it is offsetfromtheoriginbyvbll).The
shock(8c/wri
< •structure
< 10c/wri) and
there
is a dynamics
sharp
increase
in
Shock
ion
velocity
scale
in the upper
right refers to protons.AIAC
some10 %
residual te
From Burgess et al. (1989)
ll ions (solid line) and the reflected-gyrating(dashedline) and
ransmitted (dottedline) subpopulations
for (a) density;velocity
omponents
(b) Vx and (c) Vy in shockframe; (d) kinetictemerature perpendicularto magneticfield, T.L = l[2(Txx + Tyy);
nd (e) perpendicularpressure,where the thin solid line is sum
to formth
vg2• 2.15
well visible
From Sckopke et al. (1990)
ig. 6. Ion bulk parameters, normalized to their upstream vales, from simulation corresponding to Figure 4, calculated using
being gyro
In S83 it
reflected o
tosheathin
displayedi
This result illustrates how the local relative
densitiesof reflected-gyratingand transmitted ions can in
fact be very different from the overall number ratio between
the two subpopulations.We havecomputedthis latter ratio
to be almost exactly 1:3, i.e., about 25% in number of the
incident
ß
ß
o.[_
.perp
ß
ß
feature there.
difficultto
The cut on
The low
further do
mitted ions(Figure5b), givingriseto the enhanced
density
'-•-'2"T'•'-7
! ....
•-..
certainty)
ring ions a
tionof Vs
r
dication of how the subpopulationshave slightly different
turn around points: The majority of the reflectedions pass
throughvx -- 0 earlier in the shockstructurethan the trans-
o
set (cf. Ta
ied in S83
barely. Th
8, 2009
showsthis
in order of
magnetic f
from the v
from frame
are visible
havegyro
The seq
the previo
butions w
a bi-Maxw
distributio
results from
discussedi
the Mach
(horizont
marked co
15 / 1in s
tioned
Gyration and reflection: low-M shocks I
Example: Dependence on vh = vTi /vu =
V h = 0.06
0.5
0
−10
V h = 0.1
30
0
−10
40
−5
0
−5
0
−5
0
1.5
pxx
V x /V u
20
0.5
5
10
15
20
5
10
15
20
5
10
15
20
V h = 0.1
1
0.5
0
1.5
10
20
V h = 0.2
30
0
−10
40
1.5
1
pxx
V x /V u
10
1
0.5
0
−10
1
0.5
0
1.5
0
−10
V h = 0.06
1.5
1
pxx
V x /V u
1.5
p
βi /M 2
V h = 0.2
Higher vh faster
relaxation.
1
0.5
0
10
20
x/L u
Gedalin and Balikhin
30
40
0
−10
x/L u
Shock structure and ion dynamics
AIAC 8, 2009
16 / 1
Low-M 1D hybrid simulations
Left: distribution in vx − vy plane throughout the shock. Right: (top)
velocity and density (thick), (bottom) magnetic field and ion pressure
(thick). M = 1.22, θ = 80◦ , βi = βe = 0.1
M15th80b01 movie
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
17 / 1
Collisionless relaxation and magnetic oscillations
Observations: from Balikhin et al.
(2008)
0
Bn
Theory: ion pressure and magnetic
field oscillations
!5
!10
!15
40
60
80
100
120
140
160
180
200
60
80
100
120
140
160
180
200
60
80
100
120
140
160
180
200
60
80
100
120
140
160
180
200
Bm
5
0
!5
40
45
Bl
40
35
30
40
45
|B|
40
35
30
40
Time in seconds after 22:58:00
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
18 / 1
β-dependence: escaping ions - foreshock distributions,
observations
2305
09:54:06 - 09:54:54
2000
Vsw Bth
405. 12.
Bph
173.
09:54:54 - 09:55:43
Vsw Bth
405. 12.
Bph
173.
85.8
84.5
1000
2000
1000
86.5
85.0
18.6 -2000 138.3
17.0
141.1
2000
-2000
0
1000
0
1000
-1000
-2000 136.5
139.6
-2000
-1000
0
-1000
0
-1000
H. Kucharek et al.: On the origin of field-aligned beams at the quasi-perpendicular bow shock
18.1
16.7
2000
FIGURE 1. Wind/3DP ion measurements of FABs on 28 August 1995 at 93 R E .
Fig. 5. Magnetic field (top panel) and ion distribution (lower panel) in velocity space downstream, in the ramp, and upstream of the bow
shock.
Left: close to the shock, from Kucharek
etwithal.
the
to B (left of center,
pitch (2004).
angles extending Right:
to 45 . Several far
similarin
distributions
have been observed at ∼ 100 R and beyond. Clearly, these beams are unexpected at
large distances from
the
shock.
Work is now in progress to establish their source
foreshock, from such
Meziane
et
al.
(2004)
characteristics and to understand how they reach far upstream regions.
the ion distributions parallel and perpendicular to the interplanetary magnetic field (the mean magnetic field orientation is indicated by arrows) are shown for three different locations: downstream, at the ramp, and upstream of the bow
shock. The dark blue shaded areas in the plot of the magnetic
field profile indicate the integration time for the ion distributions. Downstream, the shape of the ion distribution is more
elongated in the perpendicular than in the parallel direction.
The phase space is filled with ions up to a parallel velocity of 1000 km/s. In the shock ramp gyrating ions appear,
while phase space density extends towards parallel velocity
exceeding substantially the limit of ≈1000 km/s. Upstream
of the bow shock (see right hand distribution) this part of the
distribution decouples from the core distribution and forms
a collimated beam along the mean interplanetary magnetic
field. It should be noted that the beams occupy a portion of
the phase space that is empty downstream.
Gedalin and Balikhin
2.3
Multi-spacecraft observations: a key to the basic beam
production mechanism
◦
E
Unlike single spacecraft that only provide single point measurements along the spacecraft trajectory, a multi-spacecraft
We have examined in detail the properties of fi eld aligned beams as a function
mission such as CLUSTER provides simultaneous readings
of shock geometry, taking special care to isolate the influences of ! Bn from other
at different locations. Such a measurement from the CLUSparameters
TER spacecraft taken on 2 January 2002, at
around 14:45 UT,[15]. Simple kinematic arguments lead to expectations that densities and
is shown in Fig. 6. At this time the spacecraft
a high will vary with ! , although no temperature relation immediately follows.
beamcross
speeds
Bn
Mach number shock (MA =5) with a shock normal angle of
Figure
moments computed for successive FABs observed by the Cluster/CIS
72◦ . The top and the bottom part of this figure
show 2
theshows
distributions in v⊥ vs. v$ space for SC1 andexperiment
SC4, respectively.on 23 April 2001, 0647–0651 UT. During the interval of interest no ULF
The middle part of this figure shows the energy spectra (top
waves
were observed and the IMF direction was slowly rotating toward a less radial
panel) and the magnetic field (lower panel)
of three different
spacecraft SC1, SC3, and SC4. The vertical
lines in
the specconfi
guration.
As selected, the only parameter that changed signifi cantly for this event
trograms indicate the time periods in which the distributions
was
the
angle !Bn . Successive panels show !Bn variation of the beam density normalized
have been taken. As the figure shows, spacecraft 1 is located
to the
solar
wind density (Figure 2a), the beam speed normalized to the solar wind speed
close to the bow shock, because it crosses
the shock
first.
Shock structure and ion dynamics
AIAC 8, 2009
19 / 1
Escaping ions - theory
From Burgess (1987)
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
20 / 1
β-dependence: escaping ions - mechanism
Low-Mach number oblique shocks, moderate β
Transmittedgyrating
ions
Ions reflected
non-specularly
Ions reflected
quasi-specularly
Multi-step
reflection with
escape
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
21 / 1
Figure 3.14: Upstream distribution for M = 7 in v! -v⊥ plane at five layers (x = −10,
Escaping ions - foreshock distributions, theory
−12.5, −15, −17.5 and −20) respectively.
parallel velocities (FABs).
In case of M = 7 shock, Figs. 3.19c and 3.19d demonstrate that there are two similar
populations: high energy ions with E ≈ 9.5 and pitch angles 5◦ < ψ < 20◦ and lower
energy population with E ≈ 7.5 and pitch angles 15◦ < ψ < 30◦ . As shown in all plots
each population is formed by a corresponding mechanism of escaping. Ions escaping via a
Figure
3.15: Upstream
distribution
at x =(i.e
−10(V
for different
mechanisms
of esu /Ω
u ) RGGE)
single encounter
with cross-shock
potential
RGE
and
are with
lower energies
caping
(RGE,
RGRE, RGGE,
RGGRE,
RGRRE).
M the
= 3,potential
v2 -v1 plane,
(b) M
= 3,
and larger
pitch-angles,
while the
multiple
encounter(a)with
produces
higher
venergies
M=
7, vangles
and (d) M = 7, v! -v⊥ plane.
and(c)
lower
pitch
population.
2 -v1 plane
! -v⊥ plane,
Additional information is provided in Figure 3.15. Here, the distribution at x =
−10(Vu /Ωu ) is shown for the different mechanisms of escaping. As can be seen the outer
ring population is formed by a mechanism of a single encounter with the cross-shock
potential, i.e. RGE for M = 3 and RGGE for M = 7. The inner population with
lower perpendicular velocities is formed by mechanisms RGRE for M = 3, RGGRE and
Figure 3.19:
Upstream
distributions
of energy andthat
pitch
at x encounter
= −10(Vu /Ω
RGRRE
for M
= 7. These
results demonstrate
theangle
multiple
with
the
u ) for
different mechanisms
of escaping.
M = 3ofshock:
E and (b)beams
ψ, M (FABs),
= 7 shock:
(c) the
E
cross-shock
potential leads
to formation
rather (a)
field-aligned
while
and (d)
ψ.
RGE
or RGGE
mechanisms are responsible for gyrating beams of escaping ions.
The downstream distribution of transmitted ions is shown on Fig. 3.16. In similar,
Far away from the shock front in upstream or downstream regions ions mean energy
the transformation into v1 -v2 and v! -v⊥ planes was made according to (3.4) and (3.5),
remains constant. Eventually, particles gain energy while interacting with the transition
thus for a corresponding angle of θ = 74.4◦ . As well, there was no significant dependence
layer. The energy jump of escaping ions can be explained by following. We shall look on
of distribution on the distance from the shock front, therefore the distributions are shown
Gedalin and Balikhin
Shock
structure
dynamicsof the electric field do not AIAC 8, 2009
the y-direction of ion motion,
since
neither and
x or ion
z component
From Liverts (2008, MSc thesis)
22 / 1
EDALIN ET AL. : ESCAPING IONS
Figure
6
Escaping ions
- dependence
on β
tion in v! − v⊥
distribution of
gles ψ. All dishe farthest plot
most of the ions
−3 and their per≈ 0.5. The secdensity) is in the
cond plot shows
ons with E ≈ 9
population with
ution of energies
third and fourth
osition of of Figributions do not
Figure 6. Comparison for different β with s = 0.64 and
θ = 50◦ . Left column is for β = 0.1 (efficiency 0.5%), the
middle one is for β = 0.15 (1.5%), and the right one is
for β = 0.2 (3%). Rows as in Figure 3.
From Gedalin et al. (2008)
shows the effect of β. For the chosen angle θ = 50◦ , variation of β within the low β = 0.1, 0.15, 0.2 limits does not
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
23 / 1
High-β or hot tails: acceleration
Surfing, from Lee et al. (1996)
Multiple crossing, from Zank et al.
(1996)
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
24 / 1
four times higher downstream
energy in four cycles of
reflection.
Figure 4 shows the trajectory of an ion which escapes
upstream after making a full cycle of multiple reflections,
during which vq.increases and decreases again. Figure 4a
shows that the ion trajectory does not cross the middle of
the ramp. From Fig. 4b one can see that the amplitude of
oscillations of zjx is roughly proportional
to v,., that is, the
adiabatic approximation
works quite well. It is seen also
that the reflection-escape
process is indeed almost specular in the u,v,~ plane : u,>is the same at the entry and escape
points, while v, changes its sign. As can be seen from Fig.
4c, v, in the last escape point closely corresponds
to (32).
2
Sub-structure: acceleration
s”
’2
1
0
-1
@I very sensitive to the ramp width. For the chosen
therefore
model the scales of the magnetic and electric field variations are the same and z D,. The analytical consideration
.a,
-2
-2
0
2
%l~
(c>
Fig. 3. Trajectory
of a multiply
reflected
ion escaping
down-
stream
16
4
2
0
-2
-2.0
-1.5
-1.0
-0.5
0
0.5
1.0
1.5
2.0
2.5
3.0
Xlwp,)
Fig. 2. Trajectories
of 20 ions at the high-Mach
critical quasi-perpendicular
Q = 70” shock
number
super-
Figure 5 shows the trajectory which is not covered by
the above theoretical analysis. The ion is trapped near the
ramp for some time and afterwards it becomes trapped
around
the ramp,
making
several
large amplitude
gyrations and crossing the shock front back and forth.
Eventually
it escapes upstream (high negative final v, in
Fig. 5c) having a substantial
gyration velocity.
Figure 6a shows which part of the initial pickup ion
distribution
undergoes
multiple
reflection
(for perpendicular shock geometry). In Fig. 6b we show the same
distribution
of incident pickup ions at the upstream edge
of the ramp, where it is already strongly disturbed. Almost
all multiply reflected ions are taken from the low V, part
of the distribution,
in agreement with previous theoretical
where $ = eq/(
component
of t
of the ramp), an
ion energy of d
cross-shock pote
ratio R = 2.5,
ably sufficient
regime.
Since the effi
increase of obliq
acceleration
me
nearly perpendicu
or when some s
effective width o
The dependenc
Mach number i
the shock width
Mach number.
which could pr
clusion is that
decrease with th
of the shock wid
The obtained
tra CXC~‘~(see a
to,f(v) cc up2 (an
harder than ve4
probably
attribu
actual shock stru
It should be
sitivity of the
details of the m
could be in pri
deviations from
amplitude waves
as rippling of th
any small-scale
evidence is not u
ations from the
special study w
AIAC 8, 2009paper. 25 / 1
Left: various trajectories of pickup ions. Right: efficiency
enhancement in
(b)
structured shock.
From Zilbersher and Gedalin (1997)
‘O------l
Gedalin and Balikhin
Shock structure and ion dynamics
Further evidence for local reformation of the termination shock is
provided by the qualitative transformation of the shock structure
during the ,3.9-h interval between TS-2 and TS-3 (Fig. 1). At the
front of TS-2, the bulk speed V increased continuously, rather than in
a step-like form. Instead of a simple ramp-overshoot structure in B,
there were two narrow enhancements in B resembling solitons, in
each of which there was a change in B comparable to that in the ramp
of TS-3. A shock structure at 1 AU resembling that of TS-2 was
reported in fig. 5 of ref. 26.
the vector magnetic fields in the termination shock at a rate of
2.08 samples s21, and the spacecraft was able to transmit all of this
information, making it possible to determine the complex internal structure
of the ramp shown here.
Termination shock: magnetic field
Received 19 February; accepted 15 April 2008.
1.
Burlaga, L. F. et al. Crossing the termination shock into the heliosheath: Magnetic
fields. Science 309, 2027–2029 (2005).
Decker, R. B. et al. Voyager 1 in the foreshock, termination shock, and heliosheath.
Science 309, 2020–2024 (2005).
3. Gurnett, D. A. & Kurth, W. S. Electron plasma oscillations upstream of the solar
wind termination shock. Science 309, 2025–2027 (2005).
4. Stone, E. C. et al. Voyager 1 explores the termination shock region and the
TS-3
heliosheath beyond. Science 309, 2017–2020 (2005).
0.30
a
5. Winske, D. & Quest, K. B. Magnetic field and density fluctuations at perpendicular
Ramp
NATURE | Vol 454 | 3 July 2008
Overshoot
supercritical collisionless shocks. J. Geophys. Res. 93, 9681–9693 (1988).
0.25
Foot
Undershoot
6. Lembege, B. et al. Selected problems in collisionless shock physics. Space Sci. Rev.
0.20
110, 161–226 (2004).
Solar
Heliosheath
7. Burgess, D. & Scholer, M. Shock front instability associated with reflected ions at
wind
0.15
the perpendicular
Phys. Plasmas 14, 012108 (2007).
TS-3
surface5,23. The structure of TS-4 (Fig. 1) is different
from thatshock.
of TS8. Behannon, K. et al. Magnetic field experiment
a 0.3 for Voyager-1 and Voyager-2. Space
0.10
3. In the foot region, B(t) (where t is time) appears
narrow
(1977).
Sci.as
Rev.a 21,
235–257peak,
0.48 s
9. Such
Goodrich,
C. C. in Collisionless
and the overshoot is smaller than that of TS-3.
a peak
evolves Shocks in the Heliosphere: Reviews of Current Research
0.05
(eds Tsurutani, B. T. & Stone, R. G.) 153–168
0.2 (Geophys. Monogr. Ser. Vol. 35,
from the foot as a result of bunching of reflected
solarGeophysical
wind ions
0.00
American
Union, Washington DC, 1985).
b
Shinohara, M.of
I. & Matsukiyo, S. Quasi-perpendicular shocks: Length
where they are turned back
the shock10.6,12Scholer,
. The M.,
amplitude
48 towards
s
scale of the cross-shock potential, shock reformation, and implications for shock
the
overshoot
decreases
while
the
step-like
foot
evolves
to
a
peak.
270
0.1
surfing. J. Geophys. Res. 108 (A1), doi:10.1029/2002JA009515
(2003).
These changes were observed from TS-3 to TS-4
(Fig. 1).J.The
struc11. Richardson,
D., Kasper,
J. C., Wang, C., Belcher, J. W. & Lazarus, A. J. Cool
heliosheath
deceleration of the upstream solar
Footwind at the
Ramp
Overshoot
180
ture of the termination shock evolved significantly
withinplasma
2.7 h.andThe
c
termination shock. Nature doi:10.1038/nature07024
(this issue).
0.0
360
45
small peak in B at the front of TS-4 is expected
to evolve
to a new
b studies of magnetosonic collisionless shock
12. Biskamp,
D. & Welter,
H. Numerical
Nucl. Fusion 12,pro663–666 (1972).
0
ramp on this timescale, as part of the shockwaves.
reformation
270
13. Phillips, P. E. & Robson, A. E. Influence of reflected ions on the magnetic structure
10,12,24,25
–45
cess
.
of a collisionless shock. Phys. Rev. Lett. 29, 154–157 (1972).
–90
90 in collisionless plasmas. Phys. Fluids
180
14. Leroy, M.
Structure of perpendicular
d
Reformation of the local structure of a supercritical
quasi-perpenc shocks
45
(1983).
26,
2742–2753
300
dicular shock was predicted by both hybrid and
particle
simula15. full
Woods,
L. C. On the
structure of collisionless
0 magneto plasma shock waves at
192 s
supercritical
Alfvén
tions10,13,25 for a shock with large Mms and/or a low
b, where
b Mach
is thenumbers. J. Plasma
–45 Phys. 3, 435–442 (1969).
16. Gurnett, D. A. & Kurth, W. S. Intense plasma
–90 waves at and near the solar wind
ratio of thermal pressure to magnetic pressure.
Recall that we esti200
termination shock. Nature doi:10.1038/nature07023
(this issue).
00:09
00:10
00:11
00:12
00:13
mated that Mms < 10 for TS-3. Neglecting pickup
protons,
0.04
17. Livesey,
W. A. etbal.5
ISEE
1 and 2 observations of magnetic field overshoots
in
Time (h:min,
day 244 of 2007)
quasi-perpendicular bow shocks. Geophys. Res. Lett. 9, 1037–1040 (1982).
in the solar wind upstream of TS-3, so that b 18.
might
beR.small
even if of the solar wind termination shock by non-thermal
Decker,
B.
et
al.
Mediation
100
Figure 3 | The internal structure of the ramp of TS-3. The structure is based
01:26
00:28
00:57
23:31 the 00:00
pickup protons
contribute
significantly to it.
Reformation
is a
ions.
Nature doi:10.1038/nature07030
(this issue).
on observations
oftermination
the magnetic
field strength B (a) and its directions l
(h:min)
Whang, Y. C., Burlaga,
F. Locations of the
shock and
patchy cyclicTime
shock
reformation process with a19.characteristic
timeL. F.of& Ness,(bN.) and
d (1995).
(c) at 0.48-s intervals. The magnetometer on Voyager 2 sampled
heliopause. J. Geophys. Res. 100, 17015–17023
Day 243 ofthe
2007order
2007
Day 244
of ofthe
downstream gyroperiod25. 20. Zank, G. P. et al. Interstellar pickupthe
ionsvector
and quasi-perpendicular
shocks:
magnetic fields
in the termination shock at a rate of
Implications
for
the
termination
shock
and
interplanetary
shocks.
J.
Geophys.
Res.
Furtherquasi-perpendicular
evidence for local
reformation
Figure 2 | TS-3 is a supercritical
shock.
The 48-s of the termination shock is
2.08 samples s21, and the spacecraft was able to transmit all of this
101, 457–477 (1996).
) and its directions
l (b) and d
averages of the magnetic
field strength
B (aqualitative
provided
by the
transformation
of
shock
information,
it possible
to determine the complex internal structure
21. the
Lipatov,
A. S. & structure
Zank, G. P. Pickup ion
acceleration atmaking
low b perpendicular
shocks.
the,3.9-h
192-s average
of the solar
wind speed
(c) are shown here together
Phys. Rev.
Lett.1).
82, 3609–3612
of the ramp shown here.
duringwith
the
interval
between
TS-2V and TS-3
(Fig.
At the (1999).
(d) across TS-3. The magnetic field strength profile shows the classical
22. Newbury, J. A., Russell, C. T. & Gedalin, M. The ramp widths of high-Machfrontquasi-perpendicular
of TS-2, the bulk
speed
V increased
rather
than
in
features of a supercritical
shock:
a ‘foot’,
‘ramp’, continuously,
number quasi-perpendicular collisionless shocks. J. Geophys. Res. 103 (A12),
‘overshoot’, ‘undershoot’
and smaller
oscillations,
thata order.
29581–29593
(1998).in B,
a step-like
form.
Insteadin of
simple ramp-overshoot
structure
2.
V (km s–1)
d (deg)
l (deg)
d (deg)
l (deg)
B (nT)
B (nT)
LETTERS
Supercritical profile, sub-structured ramp.
From Burlaga et al. (2008)
76
there were two narrow enhancements in B resembling solitons, in
Macmillan
Limited.to
Allthat
rights
©2008
each of which there was
a change
in Publishers
B comparable
inreserved
the ramp
of TS-3. A shock structure at 1 AU resembling that of TS-2 was
reported in fig. 5 of ref. 26.
Gedalin and Balikhin
Shock structure
Received 19 February; accepted 15 April 2008.
1.
Burlaga, L. F. et al. Crossing the termination shock into the heliosheath: Magnetic
fields. Science 309, 2027–2029 (2005).
Decker, R. B. et al. Voyager 1 in the foreshock, termination shock, and heliosheath.
Science 309, 2020–2024 (2005).
3. Gurnett, D. A. & Kurth, W. S. Electron plasma oscillations upstream of the solar
winddynamics
termination shock. Science 309, 2025–2027 (2005).
and ion
AIAC 8, 2009
2.
26 / 1
LETTERS
NATURE | Vol 454 | 3 July 2008
the heliosheath are reduced relative to those in the solar wind, except
for the two oppositely directed bursts recorded by Voyager 2 on
2007.9 and 2008.0 in Fig. 2g.
The measurements of high partial pressures of low-energy ions and
of high intensities of high-energy electrons made using the Voyager 2
LECP instrument have immediate implications for the nature and
processes of the termination shock, the foreshock and the
heliosheath. These in turn have ramifications for the global structure
of the heliosphere, particle acceleration and propagation processes, as
well as for the collisionless shock structure. Voyager 1 entered the
Termination shock peculiarity
LETTERS
termination foreshock proper at a helioradius of 85.2 AU (1 AU is the
Sun–Earth distance), and Voyager 2 did so at a helioradius of 75.3 AU,
roughly 10 AU nearer the Sun than Voyager 1. First detection by
Voyager 2 of termination shock particles around the time that the
shock swept over Voyager 1 during its inward movement is qualitatively consistent with three-dimensional heliosphere models which
predict an asymmetric termination shock that is nearer the Sun at the
position of Voyager 2 because of symmetry-breaking effects of the
interstellar magnetic field12,13. However, quantitative issues are still
under examination14.
Partial ion pressure (dynes cm–2)
TS-1
400
a
VR (km s–1)
300
200
0
Ion intensity (protons cm–2 s–1 sr–1 MeV–1)
100
b
N (cm–3)
0.006
0.004
0.002
a
10–13
10–14
b
MeV
0.028–0.043
0.043–0.080
102
0.080–0.137
0.137–0.215
0.215–0.540
101
0.54–0.99
0.99–2.14
2.14–3.50
100
10–1
0.000
–0.5
c
–0.7
c
0.043–0.080 MeV
0.54–0.99 MeV
0.137–0.215 MeV
2.14–3.50 MeV
–0.9
g(E)
106
–1.1
–1.5
105
Electron intensity
(number cm–2 s–1 sr–1 MeV–1)
T (K)
–1.3
104
103
12
14
Time (h)
16
18
Figure 5 | The termination shock is very different from other shocks
observed in the heliosphere. Voyager 2 data measured at TS-2 (crosses) at
helioradius 84 AU, in comparison with Voyager 2 data measured at
Neptune’s inbound bow shock crossing (diamonds) at helioradius 30 AU in
August 1989. The solar wind parameters upstream of Neptune are
normalized to those upstream of the termination shock; the timescales are
identical. The solar wind speed (a; Neptune data divided by 1.3) at the bow
shock fell by a factor of four but at the termination shock the speed decreased
by a factor of only two. The density (b; Neptune data divided by five) at the
bow shock increased by a factor of four, but at the termination shock by a
factor of two. The major difference is in the temperature (c; Neptune data
divided by two): at the bow shock it increased by a factor of 100, but at the
termination shock by a factor of only ten. The differences between these two
Gedalin
Balikhin
shocks are probably
caused by and
the greater
abundance of pickup ions at the
–1.7
d
0.022–0.035 MeV
103
0.035–0.061 MeV
102
0.35–1.5 MeV
101
100
2007.5
2007.6
2007.7
2007.8
2007.9
2008.0
2008.1
Time (year)
Figure 1 | Low-energy ions and electrons measured by Voyager 2 near the
termination shock during 2007. Voyager 2 crossed the termination shock at
least five times during days 242 to 244 of 2007 (refs 7–9) at helioradius
R 5 83.65 AU and heliographic latitude L 5 227.5u. a, The black trace shows
Voyager 2 0.028–3.5 MeV partial ion (proton) pressures. The blue trace
shows Voyager 1 0.040–4.0 MeV partial proton pressures, time-shifted so
that the termination shock crossing of Voyager 1 on day 351 of 2004
coincides with TS-1. Both traces exceed the magnetic field pressure
PB1 5 B12/8p (dashed red line), calculated using the mean heliosheath field
intensity B1 5 0.123 6 0.035 nT (61 s.d.) measured by Voyager 1 between
days 1 and 110 of 2005 (ref. 20). The upper and lower bounds of the vertical
error bar are PB1 evaluated respectively at B1 5 0.158 and 0.088 nT. The
Weak heating, from Richardson et al. Strong acceleration, from Decker et
(2008)
al. (2008)
Voyager 1 and 2 ion pressures were calculated using intensities of ions
arriving from the sunwards and anti-sunwards directions, to reduce
contributions from field-aligned beams that arrive mainly from the
azimuthal direction. b, Intensities in the eight Voyager 2 ion channels
calculated using proton energy passbands and efficiencies. c, Differential
spectral index c(E) evaluated at the logarithmic means of the energy
passband for the channels indicated6. d, 0.022–1.5 MeV electron intensities;
ordinate of blue trace is multiplied by 30. Electron intensities peak at or near
the termination shock, are nearly isotropic in the solar wind and heliosheath,
and at ,0.03 MeV and ,0.7 MeV are respectively higher by a factor of ,4 or
lower by a factor of ,3 than intensities of ions at the same energy. All data
shown are one-day averaged; data in c are also five-point smoothed.
68
©2008 Macmillan Publishers Limited. All rights reserved
Shock structure and ion dynamics
AIAC 8, 2009
27 / 1
SNR shocks: where goes efficiency ?
L70
GHAVAMIAN, LAMING, & RAKOWSKI
Vol. 654
High velocities ∼ 5 · 104 km/s
Low ISM magnetic field ∼ 10−6
G
Densities ∼ solar wind density
at 1 AU
Low temperatures . 104 K
High Mach numbers
Fig. 1.—Example of the optical spectrum of a Balmer-dominated shock,
showing the broad and narrow Ha lines characteristic of nonradiative shocks
in partially neutral gas. This spectrum, originally presented by Sollerman et
al. (2003), was obtained from the southwestern rim of the Galactic SNR RCW
86, with high enough spectral resolution (∼10 km s!1) to resolve the broad
(∼500 km s!1 FWHM) and narrow (∼30 km s!1 FWHM) Ha lines. The nightsky OH lines (indicated by the circled plus signs) have been left in to demonstrate their relatively narrower widths compared to the Ha lines. The broad
Ha width and ratio of the broad to narrow Ha flux for these types of shocks
were used to produce the relationship shown in Fig. 2.
IB /IN p 1.0 ! 0.2] and the northern rim [v FWHM (Ha) p
325 ! 10 km s!1; IB /IN p 1.06 ! 0.1] of RCW 86. In the fifth
SNR of our sample, DEM L71 (Ghavamian et al. 2003), we
broad component Ha width only toShock
constrainstructure
the range
Gedalin used
andtheBalikhin
Fig. 2.—Electron to proton temperature ratio at the shock front as a function
of shock velocity for five Balmer-dominated SNRs. Magnetosonic Mach numbers
(MS) appropriate for typical ISM conditions are indicated along the top axis. The
data shown here were measured from Balmer-dominated shocks in the Cygnus
Loop, RCW 86, Tycho’s SNR (Ghavamian et al. 2001), SN 1006 (Ghavamian
et al. 2002), and DEM L71 (Rakowski et al. 2003; Rakowski 2005). The dashed
error bars for RCW 86 mark previously unpublished results. Below 400 km s!1
(MS ≈ 30), the data are consistent with (Te /Tp)0 p 1 . The prediction of the proposed lower hybrid wave-heating mechanism in the cosmic ray precursor,
(Te /Tp)0 ∝ VS!2 (∝MS!2), is shown for vS 1 400 km s!1.
Higher velocities - lower efficiency of
electron heating ?
From Ghavamian et al. (2007)
perpendicular) shock is characterized not by the shock speed but
rather by the magnetosonic Mach number MS ({vS /v MS, where
v MS { (cS2 " vA2 )1/2 is the magnetosonic speed, cS is the sound
speed (p[(5/3)(P/r)]1/2) and vA [{B/(4pri )1/2] is the Alfvén
speed of the preshock gas). The preshock temperature, ion density, and magnetic field strength are not strongly constrained in
and
ion dynamics
the observed
Balmer-dominated shocks. In particular, MS AIAC
is most
8, 2009
28 / 1
Comments regarding 1D and stationarity
Not all shocks are 1D, inhomogeneity along the shock front (rippling)
may affect all reflection-gyration processes at the ramp, to less extent
downstream gyrophase mixing
Not all shocks are stationary, time-dependence may affect all
reflection-gyration processes at the ramp, as well as downstream
gyrophase mixing
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
29 / 1
Conclusions
Ion kinetic processes play the crucial role in the formation of the shock
structure
Kinetic processes may be observed at low-Mach number shocks as well
Collisionless ion heating, non-gyrotropic downstream distributions, ion
reflection, foreshock ion beams, and even acceleration at the shock
(pre-diffusion) are due to the same process - nonadiabatic ion dynamics at
the shock front.
Ion dynamics at the shock front is sensitive to the fine structure of the
shock front and initial velocities.
Gedalin and Balikhin
Shock structure and ion dynamics
AIAC 8, 2009
30 / 1