Transcript The Rice Convection Model

很汗呢！
Introduction to Magnetosphere and
MHD Modeling to S-M-I system
WangJuan
State Key Laboratory for Space Weather, CSSAR
• Magnetosphere
Outline
– Basic Structures
• 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
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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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Magnetosphere
Transportation of energy and momentum
from solar wind to Magnetosphere and
ionosphere becomes a great hot point in
the field of space physics
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Basic Structures
• Bow shock
Solar wind passing through
it would be decelerated,
compressed and heated up.
• 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
 Current
magnetosheath and magnetosphere
piece. Chapman—Ferraro current
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Magnetosphere & Solar Wind
 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.
• Magnetic tail(3 parts: tail lobe, plasma sheet, plasma sheet boundary
Estman et al
 Open
field
 Length: Several hundreds Re . Radius: about 22 Re
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 7
magnetic tail.
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 )
• Viscosity model →Oxford & Hines(1961)
– The magnetic field lines in the magnetosphere are closed. The solar
wind send its energy and momentum into the magnetosphere by
viscosity.
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– The convection electric field in the solar wind transport into the
magnetosphere, driving convection in the magnetosphere.
Magnetic reconnection
• Magnetic reconnection plays a great role in the physical
process of solar wind heating, connection between solar wind
and magnetosphere ,magnetic storms, and etc.
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.
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
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对流背景下进行并与之密切相关的。
• 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
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hypothesis
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. ←frozenin-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
Electric field Em& potential m in magnetosphere
Em  V  B  0
Plasma movement in magnetosphere
V ，，P
Deposition of energetic particle
Magnetic field
electric conductivity in the ionosphere
 
p
field-aligned current
J
H
J  E
Electric field Ei & potential i in ionosphere
▽ J  J sin I
Current in the ionosphere
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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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Magnetosphere & Ionosphere
• Incomplete coupling
• 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,
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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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Magnetosphere & Ionosphere
• Field-aligned current(Birkeland current)
• 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
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observation in the middle of 1960s.
Field Aligned Current
• The morphology of field aligned current in large scales
• Region I
A
 Down from dawn side , and up from dusk side.
 Maximum 1.5~2.5  A , dayside.
• Region II
 Opposite to region I
 Maximum 0.5~1.0  A ,nightside.
Figure . TRIAD observation
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Field Aligned Current
• 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
• 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  B  0
• modes to deal with the ionosphere
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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.
• CESE has many non-traditional features
• 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
• 3D ideal MHD equations
• Plans
• Curvilinear coordinate system
• AMR (PARAMESH)
• Divergence-free condition( powell Source Term in the
Divergence Form)
 0 


 B 
S    B
V 


V  B 


• Splitting the magnetic field to reduce the numerical error in
the divergence of B( B  B  Bd )
2
• Artificial resistance term :   B
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• Dimensionless elementary unit
基本量
符号
长度
S0
密度
磁场强度
定义
大小
备注
S0  3Re
3  (6.37 106 )m
0
0   s
1.67 1017 kg  m 3 电离层平均等离子体密度
B0
B0  Bs
3.12  10 5 T
3倍地球半径
地球赤道处磁场强度
• Solution domain and grids
• 3 Re  R  300 Re
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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• magnetic field
The first left items of the above expressions is magnetic dipole field Bd ,
the second items is mirror dipole field B ' .
• solar wind region
Bz  Bsw , Bx  By  0.
• the initial value used in the procedure
Figure. Initializing the computation region
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• inner boundary
   s , p  ps , Vn  0, Bn  2 cos  / Ri3
tangential drift velocity Vd  Ei  Bi / Bi2
equivalent extrapolation( Bt )
vm 
Em  Bm
Em  m
2
Bm
i  m
  J i  j i sin I
J i    Ei    (i )
  (  (i ))   j i sin I
j
B
 const  j i  Bi 
jm
Bm
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1
  p sin  
1 
H

(
)

(
)
2
2
Ri sin   sin I 
Ri  sin  sin I 

1
  H 
1


(
)

(

)   j i sin I
p
2
2
2
Ri sin   sin  
Ri sin  

 2

 2
f ( ) 2  g ( )  h( ) 2   p( ) j i ( ,  )



f ( )  sin 2  cos  (1  3 cos 2  ), g ( )  sin( 1  sin 2   3 cos 4  ).
h( )  4 cos  , p( ) 
3
8Ri2 sin 2   3 cos3 
 p (1  cos  )
3
1
2
cos 
sin I  
Bdr
2 cos 

Bd (1  3 cos 2  ) 12
where  p  1.2s
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• outer boundary
x  15 Re and Id=+1 inflow condition, solar wind condition
x  15 Re and Id=+1 outflow condition, equivalent extrapolation
Special dealing method to magnetic field: to compute
the total magnetic field by equivalent extrapolation
• Results
t =500
=150
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• References
Hu, Y. Q., et al. (2005), Oscillation of quasi‐steady Earth’s magnetosphere,
Chin. Phys. Lett., 22(10), 2723–2726.
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, 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.
X. C. Guo .(2006),Global MHD simulation of interaction between interplanetary
shocks and magnetosphere
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