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.