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Multifluid models of the solar wind
Leon OfmanCatholic University of America
NASA GSFC, Code 612.1, Greenbelt, MD 20771, USA
UVCS Observations of a coronal streamer
(Strachan et al 2002)
Nonthermal motions in coronal holes (SOHO/SUMER)
(Banerjee et al 1998)
Nonthermal broadening of Si VIIIContext image
WKB Alfvén wave amplitude:V~-1/4
Three-fluid model vs. UVCS observations
pO5+
r=5Rs
r=1.8Rs
Co-latitude (deg)
r=2.33Rs
180 90135
V (
km/s
)
3f model (Ofman 2000) UVCS (Strachan et al 2002)
Slow Solar WindUVCS observations vs. 3-fluid model (Ofman 2000)
UVCS Observations
O VI
Ly
Oxygen (O VI)
Protons (Ly )
Three-fluid model equations
where Zk is the charge number; Ak 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
Formation of a streamer: 3-fluid polytropic (=1.05) model with He++
R R
Formation of a streamer: 3-fluid polytropic (=1.05) model with He++
1
R [Rs]
6
R [Rs]
1
6
J2 Te
Magnetic field and flow
O5+ vs He++
O5+ He++
Heat conductive three-fluid model (e, p, He++)
“Active region” streamer model
Alfvén wave source
Alfvén wave driver is modeled by
Where ai=i-1/2, i is the ith mode, and i() is the ith random phase. The parameters are Vd=0.034 or 0.05, 1=1, N=100, N=100, <<p
Power spectrum:-1
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.
2j
Se
22
21
2
0 3
4)(
pppr
pr
p
VV
rr
V
r
VrS
krkk erSS /,0 )1(
use =10-4
use =10-4, 0~0.
Classical heat conduction is used up to 2Rs with smooth cutoff to zero for r> 2Rs
BB
BTTH kc
22/5
Alfvén wave driven fast solar wind with He++
(Ofman 2004)
Alfvén wave driven fast solar wind: 2.5D 3-fluid model: e-p-He++
R [S
olar
rad
ii]
Vp Vpr Te
1
20
1.2 1.95 1.2 1.2 1.951.95
Evolution of magnetic field Alfvénic fluctuations
|F()|2
Power spectrum at 18Rs
-2
-5/3
-Averaged radial outflow speed:3-fluid model(Ofman 2004)
p
He++O5+
p
p
p
He++
He++
H0p=0.5H0i=12Vd=0.034
H0p=0H0i=12Vd=0.05
H0p=0.5H0i=0.5Vd=0.034
H0p=0.5H0i=10Vd=0.034
Linearized multifluid equations and dispersion relation
Momentum:
Inductance:
Quasineutrality:
Dispersion Relation:
Four-fluid dispersion relation
Velocity amplitude ratios |Vi/Vp|using three fluid dispersion
He++ O6+
(Ofman, Davila, Nakariakov, and Viñas 2005, in press)
Vlasov dispersion relation for finite plasma
(Ofman, Davila, Nakariakov, and Viñas 2005, in press)
Dispersion relation from three-ion (p, He++,O6+) hybrid simulations
BVp
VHe++ VO6+
(Ofman, Davila, Nakariakov, and Viñas 2005, in press)
Velocity amplitude ratios from hybrid simulation dispersion
(Ofman, Davila, Nakariakov, and Viñas 2005, in press)
VHe++/Vp
VO6+/Vp
kCA/p~0
kCA/p=0.6
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.