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

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

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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

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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)

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

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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<

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

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1 R [R s ] 6 1 6 J2J2 TeTe

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Magnetic field and flow

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O 5+ vs He ++ O 5+ He ++

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

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“Active region” streamer model

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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

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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

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

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

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Evolution of magnetic field Alfvénic fluctuations | F ( )| 2 Power spectrum at 18R s -2 -5/3

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-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

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

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Four-fluid dispersion relation

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

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Vlasov dispersion relation for finite plasma (Ofman, Davila, Nakariakov, and Viñas 2005, in press)

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Dispersion relation from three-ion (p, He ++,O 6+ ) hybrid simulations BB VpVp V He ++ V O 6+ (Ofman, Davila, Nakariakov, and Viñas 2005, in press)

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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

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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.

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