很汗呢！

1. 很汗呢！

2. Introduction to Magnetosphere and MHD Modeling to S-M-I system WangJuan State Key Laboratory for Space Weather, CSSAR

3. Magnetosphere • Basic Structures 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

4. 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

5. Magnetosphere Transportation of energy and momentum from solar wind to Magnetosphere and ionosphere becomes a great hot point in the field of space physics

6. 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 magnetosheath and magnetosphere • Current piece.Chapman—Ferraro current

7. 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. 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. • Magnetic tail(3 parts: tail lobe, plasma sheet, plasma sheet boundary Estman et al.) • Open field • Length: Several hundreds Re . Radius: about 22 Re

8. Magnetosphere Models • 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 ) • Magnetic reconnection model →Dungey(1961) • 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. • The convection electric field in the solar wind transport into the magnetosphere, driving convection in the magnetosphere.

9. Magnetic reconnection 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. 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。

10. 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

11. 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

12. 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

13. Electric field & potential in magnetosphere Plasma movement in magnetosphere ， ，P Deposition of energetic particle electric conductivity in the ionosphere field-aligned current Magnetic field Electric field & potential in ionosphere Current in the ionosphere Magnetosphere & Ionosphere The coupling process between magnetosphere and ionosphere is complex. It can only be modeled on the basis of simplification

14. 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.

15. 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,

16. 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]

17. Magnetosphere & Ionosphere • Field-aligned current(Birkeland current) • Current flow into and out of the polar ionosphere along the magnetic field linesBirkland,1908. Horizontal current flow at 100-200km concluded from geomagnetic observation. Field-aligned current was conformed by satellite observation in the middle of 1960s.

18. 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. Field Aligned Current • The morphology of field aligned current in large scales Figure . TRIAD observation

19. 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.

20. These models are different mainly in these aspects • difference schemes • numerical grids • methods maintaining • modes to deal with the ionosphere MHD Simulations of SMI System • Current models

21. 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

22. 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 : • Plans

23. Dimensionless elementary unit • Solution domain and grids 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

24. magnetic scalar potential • initial magnetic field • magnetosphere region • combined field of the earth’s dipole field and the mirror dipole field • ( x= 15 Re)

25. The first left items of the above expressions is magnetic dipole field , the second items is mirror dipole field . • magnetic field • solar wind region • the initial value used in the procedure Figure. Initializing the computation region

26. tangential drift velocity equivalent extrapolation( ) • inner boundary

27. where

28. outer boundary and Id=+1 inflow condition, solar wind condition and Id=+1outflow condition, equivalent extrapolation Special dealing method to magnetic field: to compute the total magnetic field by equivalent extrapolation t =150 t =500 • Results

29. 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 instabilityat the magnetopause for northwardinterpl- -anetary magnetic field, J. Geophys. Res., 115, A10218,doi:10.1029/2009JA015193, 2010. X. C. Guo .(2006),Global MHD simulation of interaction between interplanetary shocks and magnetosphere • References

30. Good luck to you!