混合模拟

1. 混合模拟 基本方程与无量纲化 基本方程

2. 无量纲化 方程化为

3. 一些基本关系式

5. Bow shock and magnetosheath

6. Ion foreshock boundary Ion cyclotron waves Ions n Q-// shock Electrons B Q- shock n [after Tsurutani and Rodriguez, 1981]

7. Ion cyclotron waves downstream of quasi-perpendicular shock [From Fuselier et al. ,JGR, 1997]

8. The injection velocity can be described as Here is the compression ratio at the shock. For a supercritical, high Mach number, nearly perpendicular shock, is about 0.3 and the injection speeds for He2+ and O6+ are about and . We choose the injection speeds of He2+ and O6+ as 2.5 ( is the local Alfvén speed) and 2.9 , respectively. The injection angle is .

9. Observations of He2+ ring-beam distribution downstream of quasi-perpendicular shocks [Fuselier et al., JGR, 1997]

10. Proton and He2+ distributions from self-consistent hybrid simulations[McKean et al., 1995]

11. 1.The evolutions of velocity distributions for He2+ and other heavy ions from ring-beam distributions downstream of quasi-perpendicular shocks at different conditions(proton temperature anistropy)

12. Hybrid simulations In hybrid simulations the ions are treated kinetically while the electrons are considered as massless fluid. In our code, the particles are advanced according to the well-known Boris algorithm while the electromagnetic fields are calculated with an implicit algorithm.

13. Particles in anywhere<===>Fields in Grids interpolation Solve particles and fields self-consistently

15. Case 1: Time evolution of He2+ and O6+ temperature anisotropies

16. diagram obtained by FFT of magnetic field

17. The He2+ and O6+ velocity distributions at different times.

18. Typical trajectories of He2+ and O6+ particles. When the dispersion relation is dispersiveless, the trajectories of the particles are

19. Case 2 Time evolution of He2+ and O6+ temperature anisotropies

20. The He2+ and O6+ velocity distributions

21. Case 3 Time evolution of He2+ and O6+ temperature anisotropies

22. diagram obtained by FFT of magnetic field

23. The He2+ and O6+ velocity distributions at different times

24. Typical trajectories of He2+ and O6+ particles

25. Conclusions 1. The temperature anisotropy of protons and He2+ ring-beam distribution can excite proton cyclotron waves and helium cyclotron waves. 2. Helium cyclotron waves can scatter He2+ andO6+ from ring-beam distributions to shell-like distributions.

26. Conclusions 3. Only the waves are dominated by the helium cyclotron waves, there exist He2+ and O6+ shell-like distributions. While the waves are dominated by the proton cyclotron waves, their effects is to heat He2+ and O6+ . 4. There are observations [Fuselier, GRL, 1989], which shows the shell-like distributions for He2+ and O6+ particles. Therefore, helium cyclotron waves should exist in the downstream of quasi-perpendicular shock.

27. 2. Ion cyclotron waves in magnetosheath/plasma depletion layer

28. Formation of terrestrial plasma depletion layer(PDL) Adjacent to the sunward side of the low-shear dayside magnetopause, there exists a region characterized by reduced plasma density and increased magnetic field strength. This region is called plasma depletion layer (PDL), which is formed by the stretching of magnetic field lines and consequent pileup of the magnetic field as the magnetosheath plasma approaches the magnetopause.

29. Characteristics of magnetic fluctuations in PDL The magnetic fluctuations are predominantly transverse to the background field and their frequencies can up to the proton gyrofrequency, which are mainly electromagnetic ion cyclotron waves with left-handed polarization. The ion cyclotron waves are considered to be excited by the H+ and He2+ temperature anisotropies.

30. Ion cyclotron waves inside the PDL have three different spectral categories, called LOW, CON and BIF respectively. Anderson et al. [1994] defined these categories as follows: (1) LOW, a continuous spectrum of the ion cyclotron waves with main power below , (2) CON, a continuous spectrum with mainly power extending from up to ; (3) BIF, a spectrum characterized by two activity peaks, one above and one below.

31. Theoretical model The linear Vlasov theory can only calculate the growth rate of ion cyclotron waves excited by proton and helium temperature anisotropies. It find that the growth rate has two peaks in low beta plasma, and has only one peak in high beta plasma.

32. case 1 0.1 3.8 4.56 0.04 2 0.1 3.8 1.0 0.04 3 0.1 1.0 4.56 0.04 4 0.1 3.8 -- -- 5 0.3 3.8 4.56 0.04 6 0.3 3.8 1.0 0.04 7 0.3 1.0 4.56 0.04 Hybrid simulations To explain the generation mechanisms of the three spectral categories in the PDL,We perform one-dimensional (1-D) hybrid simulations to investigate the spectrum evolution of the ion cyclotron waves excited by the H+ and He2+ temperature anisotropies. Parameters:

33. Case 1 Time evolution of the H+ and He2+ temperature anisotropies for Run 1. The solid and dash lines represent the H+ and He2+ temperature anisotropies, respectively.

34. The frequency spectrum of the excited ion cyclotron waves during four different time periods for case 1. The solid, dash, dot and dash dot lines represent the periods, (A) from to , (B) from to , (C) from to , and (D) from to , respectively.

35. Case 2 Case 3 The frequency spectrum of the excited ion cyclotron waves during four different time periods for (a) case 2 and (b) case 3. The solid, dash, dot and dash dot lines represent the periods, (A) from to (B) from to , (C) from to , and (D)from to , respectively.

36. Case 4 The frequency spectrum of the excited waves during four different time periods for case 4, The solid, dash, dot and dash dot lines represent the periods (A) from to , (B) from to , (C) from to , and (D) from to , respectively.

37. Case 5 (a)The time evolution of the H+ and He2+ temperature anisotropies for case 5, the solid and dash lines represent the H+ and He2+ temperature anisotropies, respectively. (b) The frequency spectrum of the excited waves during four different time periods for case 5, The solid, dash, dot and dash dot lines represent the periods (A) from to , (B) from to , (C) from to , and (D) from to , respectively.

38. Case 6 Case 7 The frequency spectrum of the excited ion cyclotron waves during four different time periods for (a) case 6 and (b) case 7. The solid, dash, dot and dash dot lines represent the periods, (A) from to (B) from to , (C) from to , and (D)from to , respectively.

39. Conclusions 1. The H+ and He2+ temperature anisotropies excite the proton cyclotron waves and helium cyclotron waves, respectively. In their linear growth stage, the dominant frequency of the proton cyclotron waves is larger than the helium gyrofrequency, while the dominant frequency of the helium cyclotron waves is smaller than the helium gyrofrequency. 2. When beta is small, the BIF category is formed in the spectrum after the helium cyclotron waves are excited, which correspond to the dominant frequencies of the helium cyclotron waves and proton cyclotron waves.

40. Conclusions 3. When beta is large, the dominant frequency of the proton cyclotron waves decreases in the nonlinear stage, and their frequency band merge with that of the helium cyclotron waves after the helium cyclotron waves are excited. This can explain the CON category observed in the PDL. 4. The LOW category is formed at the quasi-equilibrium stage after their frequencies are drifted to smaller than the helium gyrofrequency.

41. 1.Ion cyclotron waves downstream of quasi-perpendicular shock(Lu et al., GRL, 32, 2005;Lu et al., JGR, 2006)2. Ion cyclotron waves in magnetosheath/plasma depletion layer(Lu, et al., JGR, 111, 2006)

42. Thank you！