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

STP seminar, 14,July, 2010

Plasma mixing of collisionless plasmas

In the MHD approximation, the frozen-in condition does not allow for plasmas to mix across magnetic field lines.

Solving the plasma mixing mechanism in the Earth’s magnetosphere leads to universal understanding of the plasma mixing in space.

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.

Dayside magnetic reconnection

Especially when IMF is southward, the solar wind plasmas can enter the magnetosphere relatively easily via dayside magnetic reconnection.

[Dungey, 1961]

The plasma mixing through the Earth’s magnetopause occurs in any IMF (magnetic field of solar wind) conditions.

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

In the LLBL, mixed ions (and electrons) are observed accompanied with bi-directionally accerelated electrons.

Particle velocity distribution functions shows the existence of bi-directional electrons in the mixing region of the LLBL. [e.g., Hasegawa et al. , 2003; Fujimoto et al., 1998]

Hot magnetospheric ions

Cold magnetosheath ions

Bi

Bi-directional electrons

GEOTAIL

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

1: magnetosphere

2: magnetosheath

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.

The vortex-induced-reconnection by two-fluid simulation [Nakamura et al., 2008]

To understand the exact mixing mechanism by the KH vortex, we first performed kinetic simulations of the vortex-induced reconnection.

Initial conditions

-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

method ： 2.5-dimensional full electromagnetic particle （ EM-PIC ） simulation [Nakamura et al., 2010]

0 40i-20i

20i

0Y

X 0 40iX

In-plane magnetic field lines Ion flow vectors

ResultsD0=2.0 (MHD-scale case),MA=4.375 (strong KHI case)

(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.

0 40i-20i

20i

0Y

X

In-plane magnetic field lines

Multiple magnetic islands

(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.

(T=30-50)The strong vortex flow produces a thin and long current.

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.

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.

(weak KHI) (strong KHI)

Generality of the multiple islands formation

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.

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.

The broadening for electrons is somewhat faster than that for ions, since the thermal speed for electrons is faster than that for ions. Plasma mixing rate of particles

initially existing at Y>0 and Y<0

ions ele.

Roles of RX in the vortex~plasma mixing~

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.

0

1

Mix

ing

rate

ions electrons

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~

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.

X

y

z

Roles of RX in the vortex~electron acceleration~

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.

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.

Summary

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.

Kinetic roles 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.

Basic properties of the vortex-induced-reconnection

Observations of the vortex-induced-reconnection

Rolled-up vortices have successfully observed by Cluster [Hasegawa et al., 2004].

Observations of the vortex-induced-reconnection

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 vortex-induced reconnection.

Electron acceleration obsercved aroud the vortex-induced RX region[Hasegawa et al., 2009]

Observations of the island formation

[Eriksson et al., 2009]

Moving magnetic islands (FTEs) were commonly observed at the hyperbolic point of the vortex flow.

Map of stream lines map from TH-A observations.

Map of stream lines and field lines map from TH-A observations.

THEMIS crossed the post-noon magnetopause.

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 vortex-induced-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~

inflowinflow /~/~ VVLT eeonaccelerati

AeeAie

onacceleratiRXe

e VVBVVm

eTE

m

eV inflow0inflow /~~

Accelerated time period

Accelerated speed

Kinetic properties of the LLBL

In the LLBL, mixed ions are observed with bi-directional electrons.

Particle velocity distribution functions shows the existence of bi-directional electrons in the mixing region of the LLBL. [e.g., Fujimoto et al., 1998]

ion

Hot

cold parallelanti-parallel

electrons

Dawn-dusk asymmetry of the LLBL

The ion mixing regions are composed of one-component ions. (hot magnetospheric and cold magnetosheath components not distinguished)

Particle velocity distribution functions shows a clear dawn-dusk asymmetry in the mixing region of the LLBL .

The ion mixing regions tend to be composed of two-component ions.⇒There is the large energy gap.

dawnside duskside

Hot

cold

PIC simulations

0

0

1,

1,

0

cc t

c t

EB J

BE

E

B

21

( ),1 /

j j j

dm qdt c

V E V BV

We have performed 2.5D relativistic electromagnetic particle-in-cell (PIC) simulations [Hoshino, 1987]. The basic equations we use are

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 velocityinverse of the ion gyrofrequency , and the ion inertial length , respectively.

000 NmBV iA

01 eBmi

iAi V

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.

, J

・・・ Equation of motion for an ion and electron

・・・ Maxwell’s equations

Earth’s Low-Latitude-Boundary-layer (LLBL)

The spacecraft ISEE-1 first detected the LLBL [Sckopke et al, 1981].The plasma mixing occurs inside the LLBL.

density

temp.

Dawn-dusk asymmetry of the LLBL

The ion mixing regions are formed from one-component ions.

[Hasegawa et al., 2003]Under prolonged northward IMF, the ion mixing regions tend to be formed from two-component ions.

dawnside duskside