Incorporating Kinetic Effects into Global Models of

the Solar Wind

Steven R. Cranmer

Harvard-SmithsonianCenter for Astrophysics

Incorporating Kinetic Effects into Global Models of

the Solar Wind

Steven R. Cranmer

Harvard-SmithsonianCenter for Astrophysics

Outline:

1. Coronal heating & solar wind acceleration

2. Preferential ion heating

3. Possible explanations from MHD turbulence

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

The extended solar atmosphere

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

The extended solar atmosphere

The “coronal heating problem”

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Solar wind acceleration• We still do not understand the processes responsible for heating the corona, but

we know that T ~ 106 K creates enough gas pressure to accelerate the solar wind.

• A likely scenario is that the Sun produces MHD waves that propagate up open flux tubes, partially reflect back down, and undergo a turbulent cascade until they are damped at small scales, causing heating.

• Cranmer et al. (2007) explored the wave/turbulence paradigm with self-consistent 1D models, and found a wide range of agreement with observations.

Z+

Z–

Z–

(e.g., Matthaeus et al. 1999)

Ulysses 1994-1995

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Coronal heating: multi-fluid, collisionless

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Coronal heating: multi-fluid, collisionless

electron temperatures

O+5O+6

proton temperatures

heavy ion temperatures

In the lowest density solar wind streams . . .

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Preferential ion heating & acceleration

Alfven wave’s oscillating

E and B fields

ion’s Larmor motion around radial B-field

• Parallel-propagating ion cyclotron waves (10–10,000 Hz in the corona) have been suggested as a “natural” energy source . . .

lower qi/mi

faster diffusion

instabilities

dissipation

(e.g., Cranmer 2001)

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

However . . .

Does a turbulent cascade of Alfvén waves (in the low-beta corona) actually produce

ion cyclotron waves?

Most models say NO!

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Anisotropic MHD turbulence• When magnetic field is strong, the basic building block of turbulence isn’t an

“eddy,” but an Alfvén wave packet. k

k

?

Energy input

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Anisotropic MHD turbulence• When magnetic field is strong, the basic building block of turbulence isn’t an

“eddy,” but an Alfvén wave packet.

• Alfvén waves propagate ~freely in the parallel direction (and don’t interact easily with one another), but field lines can “shuffle” in the perpendicular direction.

• Thus, when the background field is strong, cascade proceeds mainly in the plane perpendicular to field (Strauss 1976; Montgomery 1982).

k

kEnergy input

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Anisotropic MHD turbulence• When magnetic field is strong, the basic building block of turbulence isn’t an

“eddy,” but an Alfvén wave packet. k

kEnergy input

ion cyclotron waves

kinetic A

lfvén w

aves

Ωp/V

A

Ωp/cs

• In a low-β plasma, cyclotron waves heat ions & protons when they damp, but kinetic Alfvén waves are Landau-damped, heating electrons.

• Alfvén waves propagate ~freely in the parallel direction (and don’t interact easily with one another), but field lines can “shuffle” in the perpendicular direction.

• Thus, when the background field is strong, cascade proceeds mainly in the plane perpendicular to field (Strauss 1976; Montgomery 1982).

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Parameters in the solar wind• What wavenumber angles are “filled” by anisotropic

Alfvén-wave turbulence in the solar wind? (gray)

• What is the angle that separates ion/proton heating from electron heating? (purple curve)

k

k

θ

Goldreich &Sridhar (1995)

electron heating

proton & ion heating

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Nonlinear mode coupling?

k

k

ion cyclotron waves

k

k

Alfvén waves(left-hand polarized)

Fast-mode waves(right-hand polarized)

&

• There is observational evidence for compressive (non-Alfvén) waves, too . . .

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Preliminary coupling results• Chandran (2005) suggested that weak turbulence couplings (AAF, AFF) may be

sufficient to transfer enough energy to Alfvén waves at high parallel wavenumber.

• New simulations in the presence of “strong” Alfvénic turbulence (e.g., Goldreich & Sridhar 1995) show that these couplings may indeed give rise to wave power that looks like a kind of “parallel cascade” (Cranmer, Chandran, & van Ballegooijen 2011)

r = 2 Rs

β ≈ 0.003

Incorporating Kinetic Effects into Global Models of the Solar Wind S. R. Cranmer, SM33E-02

Conclusions

For more information: http://www.cfa.harvard.edu/~scranmer/

• Advances in MHD turbulence theory continue to help improve our understanding about coronal heating and solar wind acceleration.

• The postulated coupling mechanism is only one possible solution: see SH43D-03 (stochastic KAWs), SH54B-01 (gyrokinetic turb.), SH53A-01 (current sheets), ...

• However, we still do not have complete enough observational constraints to be able to choose between competing theories.