Generation of Nonlinear Magnetic Disturbances in the Solar Wind

1. Generation of Nonlinear Magnetic Disturbances in the Solar Wind Lin-Ni Hau (郝玲妮) B. J. Wang et al. Institute of Space Science Department of Physics National Central University, Taiwan R.O.C. 1

2. IAFA 2011 Theme ★ ★ • Nonthermal, nonextensive • Statistical physics and entropy approaches • Turbulence, complexity, nonlinear physics • Self-organization and relaxation • Instability and wave interaction • Plasma physics 2

3. Physics of B in Space Plasma • In a highly conducting plasma, the dynamics of charged particles is strongly correlated with the imbedded magnetic field. In fact, the generation and evolution as well as dissipation are the core physics of magnetized collisionless plasma. • Magnetic field perturbations or Alfven fluctuations in various spatial and temporal scales are present almost everywhere in collisionless space plasma environments. 3

4. Issue & Question • How are magnetic field perturbations generated in collisionless space plasma environments ? • What is the mechanism for smagnetic field saturation ? • To what extend the magnetic field could be deformed ? • How nonlinear and turbulent it is ? • Associated with density perturbation ? • Can the theory explain the observations ? • Two categories : Spatially uniform and geometrically nonuniform 4

5. Possible Candidates • Velocity space instability • Nonthermal equilibrium – temperature anisotropy • MHD to ion-inertia scale instabilities – Firehose and mirror instabilities 5

6. Previous Study • Nonlinear Alfven waves - steady state model • Most studies on nonlinear firehose and mirror instabilities are based on particle simulations • Lack of systematic and unified theories 6

7. Our Study & Method • MHD to ion-inertia scale firehose and mirror instabilities • Linear Theory - Vlasov, MHD and Hall MHD • Quasi-linear Theory • Nonlinear Theory 1D MHD, Hall MHD and hybrid particle simulations 2D MHD and hybrid particle simulations • Inter-comparison among various models • Identification of major physics 7

8. Observations • Temperature anisotropy in the solar wind and magnetosheath • The dependence of magnetic field fluctuations on temperature anisotropy • The dependence of magnetic field fluctuations on plasma beta 8

9. Observation in Magnetosheath temperature   p / (B2 / 20) 9 Li et al., 1994.

10. Temperature Anisotropy in the Solar Wind Histogram of solar wind spectra as a function of parallel plasma beta and temperature anisotropy. It is shown that the temperature in solar wind is nonisotropic with T|| greater than T⊥. [Kasper et al., 2002]

11. Temperature Anisotropy in the Solar Wind magnetic field plasma beta stability criterion 10

12. Generation of Temperature Anisotropy in the solar wind in the magnetosheath 12

13. Fluid Theory • Need suitable energy closure • Observational and theoretical basis • Linear theory - Instability criteria etc. • Validity of fluid theory • Prediction and new theories • Developing quasi-linear theory • Effects of ion inertia and Hall current 13

14. Energy Closure in Gyrotropic Plasmas Test of CGL and double-polytropic laws in the magnetosheath CGL : Isothermal : Others: Hau and Sonnerup; Hau et al., GRL, 1993.

15. Remarks on Energy Laws

16. Gyrotropic MHD and Hall MHD Models Energy Closure (Hau, PoP 2002) CGL : Isothermal :

17. Linear Gyrotropic MHD Theory Mirror instability : slow waves become unstable for Identical to the kinetic mirror instability criteria based on Vlasov theory

18. Linear Gyrotropic MHD Theory Standard Alfvén firehose : ( I ) ★ ★ New or slow firehose : (I> c ) Consistent with Vlasov theory for  = 2 and || = ½ ★ New or slow firehose : (c> I ) Not predicted by the Vlasov theory! Hybrid mode with maximum growth rate occurring at oblique propagation For high beta plasmas with nonadiabatic motion 18

19. Linear Gyrotropic Hall MHD Theory Parallel Firehose Instability + : whistler mode (R) -- : ion cyclotron mode (L) Independent of energy equations Unstable condition for parallel fire-hose instability: Hall current may stabilize the firehose instability ! 19

20. Linear Gyrotropic Hall MHD Theory Parallel Firehose Instability Dispersion Relation : The growth rate is slightly larger than the kinetic result. Maximum growth rate occurs at ion inertial length. Growing and propagating for unstable firehose. Stable and purely propagating for shorter wavelengths ! Wang and Hau, JGR 2010. 20

21. Alfven Firehose Instability Parallel and moderately oblique firehose instabilities are propagating and growing. Highly oblique firehose instability is purely growing ! Firehose instability becomes stable at short wavelengths.

22. Mirror Instability k = 10 λik = 10 5 5 1 0.5 0.5 0.1 1 0.1 Mirror instability is purely growing. Hall current has no or little effect !

23. MHD MHD Hall MHD Hall MHD Mirror Instability In MHD the growth rate increases with increasing k. In Hall MHD the maximum growth rate becomes a constant value at short wavelengths.

24. Magnetic Field Polarization Parallel firehose has circular, right-hand polarization. Oblique firehose is more linearly polarized. Mirror instability is linearly polarized.

25. Quasi-Linear Theory Parallel firehose instability

26. Nonlinear Theory • 1D MHD Model – mirror and firehose • 1D Hall MHD Model – mirror and firehose • 1D Hybrid Particle Simulation – mirror and firehose • 2D Hybrid Particle Simulation – mirror and firehose 26

27. Magnetic Hole Structure

28. Mirror Instability magnetic field depression density enhancement

29. Oblique Slow Firehose Instability density enhancement magnetic field depression 29

30. Magnetic Field Oscillation

31. 1D Hybrid Particle Simulations Parallel firehose instability Oscillatory feature may disappear for very large pressure anisotropy. 31

32. 1D Hall MHD Simulation Parallel firehose : Oscillatory and damping behavior of magnetic field may be reproduced by the Hall MHD model but only for single-mode perturbation and small Hall parameter. 32

33. 1D MHD Simulations Parallel firehose : Damping or Diffusion due to Oscillatory and damping behavior of magnetic field may be reproduced by the MHD model which is not associated with wave-wave coupling. 33

34. Saturated Magnetic Field

35. Parallel Firehose Instability Hall MHD model Saturated magnetic field is not sensitive to the form of initial perturbations.

36. Firehose Instability - Hall MHD Model h = 5, Random mode

37. Firehose Instability

38. Mirror Instability : Hall MHD Model

39. Magnetic Hodogram

40. Parallel Firehose Instability – Hall MHD Model R.H.P 40

41. Firehose Instability : Hall MHD Model h = 5 30o dBFL 30o dBFL 60o dBFL

42. Firehose Instability : Hall MHD Model h = 0.5

43. Firehose Instability : Hall MHD Model h = 5, Random mode 30o dBFL 30o dBFL 60o dBFL

44. Mirror Instability : Hall MHD Model

45. Magnetic Field Spectrum

46. Paralle Firehose Instability : Hall MHD Model Single mode Two-mode Four-mode random

47. Paralle Firehose Instability : 1D Hybrid Simulation 47

48. Time Evolution

49. Firehose Instability: Hall MHD Model (single mode) h = 5 30o 60o

50. Firehose Instability: Hall MHD Model h = 5, Random mode 30o 60o