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Introduction to Magnetosphere and MHD Modeling to S-M-I system

WangJuanState Key Laboratory for Space Weather, CSSAR

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Outline

• Interaction Between Magnetosphere and Solar Wind – Magnetosphere Models– Reconnection

Around the subsolar point

Polar cusp

Magnetic tail

– K‐H Instability

• Coupling between Magnetosphere and Ionosphere• MHD Simulations of SMI System• What has been done

– Basic Structures

• Magnetosphere

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Magnetosphere Under the effect of the solar wind ， the intrinsic magnetic field of

the earth forms a natural protective barrier. In magnetosphere, there are many complex natural phenomena, such as reconnections,magnetic storms, auroras and etc.

Figure 1. Configuration of the magnetosphere in the noon-midnight meridian

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Transportation of energy and momentum

from solar wind to Magnetosphere and

ionosphere becomes a great hot point in

the field of space physics

Magnetosphere

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• Magnetosheath Between bow shock and magnetopause. Compared with magnetosphere, it has high plasma density and low magnetic intensity

• Magnetopause boundary (transition region into the magnetosphere)

Between magnetosheath and magnetosphere

Current piece. Chapman—Ferraro current

Basic Structures• Bow shock Solar wind passing through it would be decelerated, compressed and heated up.

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Magnetosphere & Solar Wind

The main body of the solar wind cannot pass through the magnetopause

directly. The velocity is decelerated to subsonic speed. Then the solar wind

pass around the magnetopause. It compresses the dayside of the magneto-

-pause and stretches the night side of the magnetopause to form the

magnetic tail.

Its position is mainly controlled by magnetic pressure of magnetosheath and dynamical pressure of the solar wind.

Magnetic storms with sudden commencements (ssc) occurs when there are IMF shocks or discontinuities ( kinetic pressure of the solar wind increases suddenly), the magnetic field on the ground increases dozens of nTs because of the compression of the magnetopause.

Open field Length: Several hundreds Re . Radius: about 22 Re

• Magnetic tail(3 parts: tail lobe, plasma sheet, plasma sheet boundary Estman et al.)

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Magnetosphere Models• Magnetic reconnection model →Dungey(1961) Southern IMF

– Dayside of the magnetosphere. →open the closed magnetic

lines and magnetic lines transport towards the tail. The convection electric field in the solar wind transport into the magnetosphere,

driving convection in the magnetosphere. – Geomagnetic tail →earthward plasma flow & tailward plasma flow

Northern IMF

Polar cusp ( dayside is compressed & night side stretches towards the tail )

– The magnetic field lines in the magnetosphere are closed. The solar wind send its energy and momentum into the magnetosphere by viscosity.– The convection electric field in the solar wind transport into the magnetosphere, driving convection in the magnetosphere.

• Viscosity model →Oxford & Hines(1961)

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The reconnection model proposed by Dungey was validated by observation. It provided a physical mechanism that transform the magnetic energy into kinetic energy and thermal energy quickly.

• Magnetic reconnection plays a great role in the physical process of solar wind heating, connection between solar wind and magnetosphere ,magnetic storms, and etc.

Magnetic reconnection

从 1961 年至今，对磁层是开放还是闭合，对粘性和重联作用的重要性及具体机制有过很多讨论，也存在不少有待解决的问题。但各种观测都肯定了对流运动的存在，并证实了它是磁层的基本物理过程。而磁层和电离层中的种种现象正是在此对流背景下进行并与之密切相关的。

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• Multi-spacecraft in situ observations were used to infer the global geometry of the magnetic merging line, or X line (Paschmann [2008]).

• Phan et al.[2006] used the Geotail and Wind data during stable dawn ward dominated IMF to infer the presence of a tilted X line hinged near the sub-solar point.

• On the basis of a statistical study of 290 fast flow events measured by Double Star/TC-1 in low latitudes and Cluster in high latitudes, a possible S-shaped X line exists for generic dawn ward IMF cases [Pu et al. 2007]. The configuration of the merging line inferred from these observations is consistent with the prediction from the component reconnection hypothesis

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K‐H Instability

Figure 1 shows color contours of the physical parameters of an unsteady magnetosphere in the equatorial plane, including the x and y components of the velocity (vx, vy), the total velocity (v), the logarithm of the number density (log10[n(cm−3)]), the thermal pressure (log10[P(nPa)]) and the magnetic field (log10[ B (nT)]). ∣ ∣

The bow shock and the magnetopause intersect with the Sun‐Earth line at about x =14RE and 10 RE, respectively

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K‐H Instability • Mechanism -Velocity shear layer across the magnetopause. -Corresponding surface waves. The surface wave increases roughly from 1 RE (at the beginning) to 8 RE (flank region) . - Many vortices are generated along the magnetopause point from the dayside region to the magnetotail, along the direction of the flows near the magnetopause. The magnetopause boundary appears to be wavelike at the flank region.

Conclusion: The solar wind momentum and energy is then transported into the magnetosphere directly. ←frozen-in-flux condition

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Magnetosphere & Ionosphere

The coupling process between magnetosphere and ionosphere is complex. It can only be modeled on the basis of simplification

0mE V B ������������������������������������������

Magnetic field

Electric field & potential in magnetospheremE m

electric conductivity in the ionosphere

p H

Plasma movement in magnetosphere， ， P

Electric field & potential in ionosphereiiE Current in the ionosphere

J E������������������������������������������

field-aligned current J

sinJ J I

����������������������������▽

Deposition of energetic particle

V

��������������

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Magnetosphere & Ionosphere

• Hypothesis

• In the region between inner boundary of magnetosphere and ionosphere, dipole field is dominant.

• Electrical potential is equi-potential along magnetic field lines.

Solve an elliptic equation to obtain the distribution of the

electric potential in the ionosphere.(MUDPACK)

• Movement in magnetosphere → currents→ closing with the current in ionosphere ← electric conductivity is the key

Pedersen conductivity (uniform distribution), Hall conductivity is ignored.

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• Mapping error of electric field. Potential difference between magnetosphere and corresponding ionosphere point.

• Presence of parallel electric fields.

• Deposition of energetic particle from magnetosphere into ionosphere and Solar ultraviolet radiation. increase the electric conductivity in auroral zone, so then affects the distribution of current and electric field in the ionosphere, thereby influences electric field and current in the magnetosphere.

• Electric conductivity in the ionosphere increases. when the high speed electron flow accelerates,

• Incomplete coupling

Magnetosphere & Ionosphere

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Magnetosphere & Ionosphere

• Coupling process(2 kinds)

• self-consistent [RCM, Wolf and Kanmide,1983]

• key parameters separated

• Intensive study RCM [Darren L.De Zeeuw et al.,2004]

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• Field-aligned current(Birkeland current)

Magnetosphere & Ionosphere

• Current flow into and out of the polar ionosphere along the magnetic field lines Birkland,1908.

Horizontal current flow at 100-200km concluded from geomagnetic observation.

Field-aligned current was conformed by satellite observation in the middle of 1960s.

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Field Aligned Current

• The morphology of field aligned current in large scales

A

Figure . TRIAD observation

• Region I

Down from dawn side , and up from dusk side.

Maximum 1.5~2.5 , dayside.

• Region II

Opposite to region I

Maximum 0.5~1.0 ,nightside.A

A

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• The magnetic field intensity of IMF and the force exerted upon the earth by the solar wind determine some characters of region 1 and 2 field aligned current.

Southern density of the currents increases. Northern

Field Aligned Current

• very strong north Bz effect. Flow direction of NBz is opposite to region 1 current. • modulated by By. By>0 ， northern cusp region dominated by current flowing out, southern cusp region dominated by current flowing in; By<0, opposite.

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MHD Simulations of SMI System• Current models

Simulation method Author & year

TVD J.G.Lyon et al.(2004)

Lax-Wendroff Ogino et al.(1994)

FV-TVD Tanaka(1994)

BATS-R-US Gombosi(1996)

PPMLR-MHD Hu et al.(2005)

Leap-Frog T.Ogino(2004)

• These models are different mainly in these aspects• difference schemes

• numerical grids

• methods maintaining

• modes to deal with the ionosphere

0B ��������������

What has been done

• What I will do is using CE/SE + MHD method to model the stable magnetosphere under the steady effects of the solar wind.

• a unified treatment of space and time• conservation elements (CEs) and solution elements (SEs)• solving the physical variables and their spatial derivatives simultaneously• a novel shock capturing strategy without using Riemann solvers

• CESE has many non-traditional features

• 3D ideal MHD equations

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• Plans

• Curvilinear coordinate system• AMR (PARAMESH)• Divergence-free condition( powell Source Term in the Divergence Form)

• Splitting the magnetic field to reduce the numerical error in the divergence of ( )

• Artificial resistance term :

dBBB B

BV

V

BBS

0

B2

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• Dimensionless elementary unit

基本量 符号 定义 大小 备注

长度 3 倍地球半径

密度 电离层平均等离子体密度

磁场强度 地球赤道处磁场强度

eRS 30

0

0B sBB 0

0S m)1037.6(3 6

3171067.1 mkg

T51012.3

s 0

• Solution domain and grids• Re300Re3 R

内边界以下的区域从解域中剔除，一方面是为了避免 Alfven 速度过高，另一方面是该区域内地球自转和等离子体动力论效应起重要作用，不适合采用单纯的 MHD 描述。

• initial conditions

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• initial magnetic field

• magnetosphere region

combined field of the earth’s dipole field and the mirror dipole field

( x= 15 Re)

• magnetic scalar potential

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• solar wind region.0, yxswz BBBB

• the initial value used in the procedure

• magnetic field

The first left items of the above expressions is magnetic dipole field ,

the second items is mirror dipole field .

dB

'B

Figure. Initializing the computation region

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• inner boundary

3n /cos2,0V,, inss RBpp

2/ iiid BBEV tangential drift velocity

tBequivalent extrapolation( )

2

m

mmm

B

BEv

mmE

m

m

iiB

jBjconst

B

j

IjJ ii sin

)( iii EJ Ij ii sin))((

mi

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),()()()()(2

2

2

2

ijphgf

).cos3sin1sin()(),cos31(cossin)( 4222 gf

cos)cos1(

cos3sin8)(,cos4)(

213

3223

p

iRph2

12 )cos31(

cos2sin

d

dr

B

BI

)sinsin

(1

)sin

sin(

sin

122

IRIRHp

ii

IjRR ip

H

ii

sin)(sin

1)

sin(

sin

1222

sp 2.1where

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• outer boundary

Re15x

Re15x

and Id=+1 inflow condition, solar wind condition

and Id=+1 outflow condition, equivalent extrapolation

Special dealing method to magnetic field: to compute the total magnetic field by equivalent extrapolation

• Results

t =150 t =500

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• ReferencesHu, Y. Q., et al. (2005), Oscillation of quasi‐steady Earth’s magnetosphere,Chin. Phys. Lett., 22(10), 2723–2726.

X. C. Guo, C. Wang, and Hu, Y. Q. (2007), Global MHD simulation of the Kelvin‐Helmholtz instability at the magnetopause for northward interpl--anetary magnetic field, J. Geophys. Res., 115, A10218, doi: 10.1029/ 2009 JA015193, 2010.

Ogino, T. (1986), A three‐dimensional MHD simulation of the interaction of the solar wind with the Earth’s magnetosphere: The generation of field – aligned currents, J. Geophys. Res., 91(A6), 6791–6806.

Tanaka, T., Configurations of the solar wind flow and magnetic field around the planets with no magnetic field: Calculation by a new MHD simulation scheme, J. Geophys. Res., 98, 17251, 1993.

X. C. Guo .(2006),Global MHD simulation of interaction between interplanetaryshocks and magnetosphere

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