Download Kinetic aspects of the vortex-induced

STP seminar, 14,July, 2010
Kinetic properties of magnetic reconnection
induced by the MHD-scale Kelvin-Helmholtz
vortex: particle simulations
中村 琢磨 (T.K.M. Nakamura)
Collaboraters:
H. Hasegawa, I. Shinohara, and M. Fujimoto
Plasma mixing of collisionless plasmas
In the MHD approximation, the frozen-in condition does
not allow for plasmas to mix across magnetic field lines.
BUT, for example, the Earth’s magentosphere contains
plasmas of solar wind origin.
⇒It means plasma mixing in fact occurs through the Earth’s
magnetopause.
Solving the plasma mixing mechanism in the Earth’s
magnetosphere leads to universal understanding of the
plasma mixing in space.
Dayside magnetic reconnection
The plasma mixing through the Earth’s magnetopause
occurs in any IMF (magnetic field of solar wind) conditions.
Especially when IMF is southward, the solar wind plasmas
can enter the magnetosphere relatively easily via dayside
magnetic reconnection.
[Dungey, 1961]
Earth’s Low-Latitude-Boundary-layer (LLBL)
Even when IMF is northward, the plasma mixing occurs
in the low-latitude boundary layer (LLBL).
[e.g., Mitchell et al., 1987; Hasegawa et al., 2003].
Kinetic properties of the LLBL
 Particle velocity distribution functions shows the existence of bidirectional electrons in the mixing region of the LLBL.
[e.g., Hasegawa et al. , 2003; Fujimoto et al., 1998]
Hot magnetospheric ions
Cold magnetosheath ions
GEOTAIL
Bi-directional electrons
Bi
In the LLBL, mixed ions (and electrons) are observed accompanied with
bi-directionally accerelated electrons.
How to form the LLBL?
[Song & Russell, 1992]
[Hasegawa et al., 2004]
To explain how to form the LLBL under northward IMF, two major candidates have
been given,
1. double lobe reconnection at the high-latitude ⇒dayside LLBL?
2. Kelvin-Helmholtz vortices at the low-latitude. ⇒tail-flank LLBL?
BUT, the exact mixing mechanism by KH vortices has not yet been solved.
The KH vortex
2: magnetosheath
1: magnetosphere
The vortex-induced-reconnection by two-fluid simulation
[Nakamura et al., 2008]
Generally, a velocity boundary like the magnetopause is also a magnetic boundary.
⇒Past Linear analyses have shown that the Kelvin-Helmholtz vortex grows at the
magnetopause almost always accompanied with magnetic reconnection (that is,
the vortex-induced reconnection). [T.K.M. Nakamura et al., 2008]
The vortex-induced reconnection can lead to the plasma mixing along reconnected
field lines.
⇒The vortex-induced reconnection may form the LLBL.
To understand the exact mixing mechanism by the KH vortex,
we first performed kinetic simulations of the vortex-induced reconnection.
Initial conditions
method：2.5-dimensional full electromagnetic particle （EM-PIC） simulation [Nakamura et al., 2010]
-Initial parameters・N0=Ni0=const
・Bz0=4*B0 =const
・Bx0=B0*tanh(Y/D0) （current sheet）
・Vx0=V0*tanh(Y/D0) （velocity shear layer）
・D0=4.0, 2.0,1.0 [λi] (MHD-scale boundary layer)
・MA=V0/VA0=2.5(weak KHI)~5.0(strong KHI)
(KHI can grow when MA>2 [Miura & Pritchett, 1982] )
・Lx=λKH=20D0
(=fastest growing KH mode [Miura & Pritchett, 1982] )
・Ti/Te=1/8
・Mi/Me=25,100
・ωpe/Ωe=2.0
・100 particles/cell
Results
D0=2.0 (MHD-scale case),MA=4.375 (strong KHI case)
20li
In-plane magnetic field lines
Ion flow vectors
Y0
-20li
0
X
40li 0
X
40li
(T<50)The KHI grows and locally compresses the current sheet.
(T~50)Multiple reconnection occurs at the compressed thin current sheet.
(T~80)Finally, the KH vortex is highly rolled-up as a large magnetic island.
Multiple magnetic islands
In-plane magnetic field lines
20li
Y0
-20li
0
X
40li
(T=30-50)
The strong vortex flow produces a thin and long current.
(T=60-80)
Multiple magnetic islands are formed and move toward the main body of the
vortex.
(T~80)
Multiple magnetic islands are incorporated in turn into the vortex body via the
re-reconnection process.
Generality of the multiple islands formation
When Lcs>Lisland, more than one magnetic island can appear.
Since Lcs~5D0, and Lisland~12dmin,
the formation condition of magnetic islands is dmin/D0<0.4.
As D0, or MA decreases, dmin/D0 increases.
BUT, even in the smallest set of (D0,MA), dmin/D0<<0.4.
⇒The multiple islands formation can generally occur.
Generality of the multiple islands formation
(weak KHI)
(strong KHI)
Actually, in all cases, more than two magnetic islands appear.
The generation of multiple magnetic islands is a general feature
of the vortex-induced-reconnection.
Roles of RX in the vortex
Generally, reconnection can cause
1.the plasma mixing
2.the particle acceleration.
We investigated how the vortex-induced reconnection causes
the plasma mixing and particle acceleration processes.
ions
ele.
Roles of RX in the vortex
~plasma mixing~
(T~60-)
Both ions and electrons across the velocity
shear layer begin to mix from multiple X-lines.
(T~60-90)
The mixing area broadens along reconnected
field lines by the thermal speed.
(T=120)
Finally, inside of the vortex (island) becomes
filled with the well-mixed ions and electrons.
Plasma mixing rate of particles
initially existing at Y>0 and Y<0
The broadening for electrons is somewhat
faster than that for ions, since the thermal speed
for electrons is faster than that for ions.
Roles of RX in the vortex
~plasma mixing~
Mixing rate
1
ions
electrons
0
The mixing area broadens efficiently inside the
multiple magnetic islands.
Since the islands with well-mixed plasmas are
incorporated into the vortex body via re-RX,
the plasma mixing rapidly progresses while
the islands incorporation process continues.
(a) Total number of the mixed cells.
(b) Sketch of the plasma mixing process in
single X-line and multiple X-lines cases.
Roles of RX in the vortex
~electron acceleration~
Around the RX-points, the negative
reconnection electric field appears.
Around the re-RX points, the
positive reconnection electric field
appears.
Each reconnection electric field
intensity is almost consistent with the
reconnection rate at each
reconnection point (not shown).
Roles of RX in the vortex
~electron acceleration~
y
z
X
At RX-points, electrons are accelerated in the +Z-direction (almost same as the
parallel direction) by the negative reconnection electric field.
At re-RX points, electrons are accelerated in the -Z-direction (almost same as the
anti-parallel direction) by the positive reconnection electric field.
Roles of RX in the vortex
~electron acceleration~
Grid number normalized by the total grid number of
(red) the ion mixing area,(blue) electron mixing
area, (green) both ion and electron mixing area,
and (purple ) the area where plasma mixing and
bi-directional electrons coexist.
Since the re-RX process mixes electrons accelerated in the +Z and –Z directions,
inside of the vortex body is filled with the bi-directionally accelerated electrons.
⇒Mixed plasmas and bi-directional electrons inevitably
coexist inside the rolled-up vortex via a series of multiple
islands formation and incorporation processes.
Summary
Basic properties of the vortex-induced-reconnection
 Multiple magnetic islands are generally formed at the
compressed thin current sheet by the vortex flow.

These islands are incorporated into the vortex body
via the re-reconnection process.
Kinetic roles of the vortex-induced-reconnection
 The plasma mixing caused by the vortex-induced-reconnection is enhanced
by a series of multiple islands formation and incorporation processes.
 Bi-directional accelerated electrons are produced inside the vortex
by a series of multiple islands formation and incorporation processes.
 Thus, mixed plasma and bi-directional electrons (which are
the same features as the LLBL plasmas) inevitably coexist inside
the rolled-up vortex.
Observations of the vortex-induced-reconnection
Rolled-up vortices have successfully observed by Cluster [Hasegawa et al., 2004].
Observations of the vortex-induced-reconnection
Electron acceleration obsercved
aroud the vortex-induced RX region
[Hasegawa et al., 2009]
C1-C4 crossed a same current sheet between KH
vortices around 20:35:00UT.
C3 observed the evidence of reconnection.
C4 observed a bipolar BN fluctuation just after the CS
crossing!!
⇒This BN fluctuation could be the direct evidence of
the multiple islands formation process of the vortexinduced reconnection.
Observations of the island formation
THEMIS crossed the post-noon magnetopause.
Map of stream lines map from TH-A observations.
Moving magnetic islands (FTEs) were
commonly observed at the hyperbolic point of
the vortex flow.
[Eriksson et al., 2009]
Map of stream lines and field lines map from TH-A observations.
Roles of RX in the KH vortex
~mixing with bidirectional ele.~
What controls the thickness of the current sheet?
In ideal-MHD simulations, the current
sheet can become thinner at the
thickness of dx.
In particle simulations, before the
current sheet thickness reaches dx,
magnetic reconnection occurs.
⇒The lower limit of the current sheet
thickness is controlled by the vortexinduced-reconnection process.
What controls the thickness of the current sheet?
As the KHI grows, the current sheet
becomes thinner and thus the RX (tearing
instability) growth rate increases.
←The RX growth rate depends on the current
sheet thickness.
When the RX growth rate exceeds the KHI
growth rate (T~48), the linear growth of the
KHI finish and at the same time the current
sheet thinning begins to stop.
⇒The KHI growth rate controls
the minimum thickness of the
current sheet.
Roles of RX in the KH vortex
~electron acceleration~
Accelerated time period
Tacceleration ~ Le / Vinflow ~ le / Vinflow
Accelerated speed
Ve ~
e
e
 E RX  Tacceleration ~
 Vinflow  V Ai  B0  l e / Vinflow  V Ae
me
me
Kinetic properties of the LLBL
 Particle velocity distribution functions shows the existence of bidirectional electrons in the mixing region of the LLBL.
[e.g., Fujimoto et al., 1998]
electrons
ion
cold
anti-parallel
parallel
Hot
In the LLBL, mixed ions are observed with bi-directional electrons.
Dawn-dusk asymmetry of the LLBL
 Particle velocity distribution functions shows a clear dawn-dusk
asymmetry in the mixing region of the LLBL .
dawnside
duskside
cold
Hot
The ion mixing regions are composed of
one-component ions.
(hot magnetospheric and cold
magnetosheath components not distinguished)
The ion mixing regions tend to be
composed of two-component ions.
⇒There is the large energy gap.
PIC simulations
We have performed 2.5D relativistic electromagnetic particle-in-cell (PIC) simulations
[Hoshino, 1987]. The basic equations we use are
1 E
   B  c 0 J ,
c t
1 B
   E,
c t

E 
0
・・・Maxwell’s equations
B  0
, J
mj
d
1
 Vj   q(E  Vj  B),  

2
dt
1 V / c
・・・Equation of motion for an ion and electron
where  is the Lorentz factor, c is the speed of light and the suffix j is the particle number.
The charge density  and the current density J is calculated by the PIC method.
Using initial density N0 and in-plane magnetic field B0, normalizations are made as follows:
the velocity, time, and length are normalized by the ion Alfven velocity VA  B0 mi N 0  0
inverse of the ion gyrofrequency  1  mi eB0 , and the ion inertial length li  V A  i ,
respectively.
Earth’s Low-Latitude-Boundary-layer (LLBL)
density
temp.
The spacecraft ISEE-1 first detected the LLBL
[Sckopke et al, 1981].
The plasma mixing occurs inside the LLBL.
Dawn-dusk asymmetry of the LLBL
dawnside
duskside
[Hasegawa et al., 2003]
The ion mixing regions are formed
from one-component ions.
Under prolonged northward IMF,
the ion mixing regions tend to be
formed from two-component ions.