1. Multifluid models of the solar wind Leon Ofman Catholic University of America NASA GSFC, Code 612.1, Greenbelt, MD 20771, USA

2. UVCS Observations of a coronal streamer (Strachan et al 2002)

3. Nonthermal motions in coronal holes (SOHO/SUMER) (Banerjee et al 1998) Nonthermal broadening of Si VIII Context image WKB Alfvén wave amplitude:  V~  -1/4

4. Three-fluid model vs. UVCS observations p O 5+ r=5R s r=1.8R s Co-latitude (deg) r=2.33R s 180 90 135 V (km/s) 3f model (Ofman 2000) UVCS (Strachan et al 2002)

5. Slow Solar Wind UVCS observations vs. 3-fluid model (Ofman 2000) UVCS Observations O VI Ly  Oxygen (O VI) Protons (Ly  )

6. Three-fluid model equations where Z k is the charge number; A k is the atomic mass number of species k. Normalized three fluid equations for V<<c, with gravity, resistivity, viscosity, and Coulomb friction, neglecting electron inertia, assuming quasi-neutrality:  k =5/3

7. Formation of a streamer: 3-fluid polytropic (  =1.05) model with He ++ RR  

8.  1 R [R s ] 6 1 6 J2J2 TeTe

9. Magnetic field and flow

10. O 5+ vs He ++ O 5+ He ++

11. Heat conductive three-fluid model (e, p, He ++ )

12. “Active region” streamer model

13. Alfvén wave source Alfvén wave driver is modeled by Where a i =i -1/2,  i is the i th mode, and  i (  ) is the i th random phase. The parameters are V d =0.034 or 0.05,  1 =1,  N =100, N=100,   <<  p Power spectrum:  -1

14. Heating terms Electron heating by current dissipation: Proton heating by viscous dissipation: Empirical heating term for ions: Heat Conduction is included for protons and electrons along the magnetic field. use  =10 -4 use   =10 -4,  0 ~0. Classical heat conduction is used up to 2R s with smooth cutoff to zero for r> 2R s

15. Alfvén wave driven fast solar wind with He ++ (Ofman 2004)

16. Alfvén wave driven fast solar wind: 2.5D 3-fluid model: e-p-He ++  R [Solar radii] VpVp V pr TeTe 1 20 1.2 1.95 1.2 1.95

17. Evolution of magnetic field Alfvénic fluctuations | F (  )| 2     Power spectrum at 18R s  -2  -5/3

18.  -Averaged radial outflow speed:3-fluid model (Ofman 2004) p He ++ O 5+ p p p He ++ H 0p =0.5 H 0i =12 V d =0.034 H 0p =0 H 0i =12 V d =0.05 H 0p =0.5 H 0i =0.5 V d =0.034 H 0p =0.5 H 0i =10 V d =0.034

19. Linearized multifluid equations and dispersion relation Momentum: Inductance: Quasineutrality: Dispersion Relation:

20. Four-fluid dispersion relation

21. Velocity amplitude ratios |V i /V p | using three fluid dispersion He ++ O 6+ (Ofman, Davila, Nakariakov, and Viñas 2005, in press)

22. Vlasov dispersion relation for finite  plasma  (Ofman, Davila, Nakariakov, and Viñas 2005, in press)

23. Dispersion relation from three-ion (p, He ++,O 6+ ) hybrid simulations BB VpVp V He ++  V O 6+  (Ofman, Davila, Nakariakov, and Viñas 2005, in press)

24. Velocity amplitude ratios from hybrid simulation dispersion (Ofman, Davila, Nakariakov, and Viñas 2005, in press) V  He ++ /V  p V  O 6+ /V  p kC A /  p ~0 kC A /  p =0.6

25. Conclusions Recent observations of minor ion emission lines in coronal holes provide clues for the acceleration and heating mechanism of the fast wind, and require multi-fluid and kinetic modeling in order to interpret the results. The slow solar wind has been modeled with 2D three-fluid code, and the basic features of streamers and acceleration profiles are recovered for protons and heavy ions. Wave driven wind in coronal holes was modeled with the three-fluid code in a self-consistent model, and the different proton and heavy ions flow profiles are reproduced. High frequency waves (in the ion-cyclotron frequency range) produce different perpendicular velocities for protons and heavy ion in the multifluid model, as well is in the hybrid simulations.