1. Incorporating Kinetic Effects into Global Models of the Solar Wind Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

2. Incorporating Kinetic Effects into Global Models of the Solar Wind Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics Outline: 1.Coronal heating & solar wind acceleration 2.Preferential ion heating 3.Possible explanations from MHD turbulence

3. Incorporating Kinetic Effects into Global Models of the Solar WindS. R. Cranmer, SM33E-02 The extended solar atmosphere

4. Incorporating Kinetic Effects into Global Models of the Solar WindS. R. Cranmer, SM33E-02 The extended solar atmosphere The “coronal heating problem”

5. Incorporating Kinetic Effects into Global Models of the Solar WindS. R. Cranmer, SM33E-02 Solar wind acceleration We still do not understand the processes responsible for heating the corona, but we know that T ~ 10 6 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–Z– Z–Z– (e.g., Matthaeus et al. 1999) Ulysses 1994-1995

6. Incorporating Kinetic Effects into Global Models of the Solar WindS. R. Cranmer, SM33E-02 Coronal heating: multi-fluid, collisionless

7. Incorporating Kinetic Effects into Global Models of the Solar WindS. R. Cranmer, SM33E-02 Coronal heating: multi-fluid, collisionless electron temperatures O +5 O +6 proton temperatures heavy ion temperatures In the lowest density solar wind streams...

8. Incorporating Kinetic Effects into Global Models of the Solar WindS. 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 q i /m i faster diffusion instabilities dissipation (e.g., Cranmer 2001)

9. Incorporating Kinetic Effects into Global Models of the Solar WindS. 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!

10. Incorporating Kinetic Effects into Global Models of the Solar WindS. 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

11. Incorporating Kinetic Effects into Global Models of the Solar WindS. 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 k Energy input

12. Incorporating Kinetic Effects into Global Models of the Solar WindS. 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 ion cyclotron waves kinetic Alfvén waves Ω p /V A Ω p /c s 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).

13. Incorporating Kinetic Effects into Global Models of the Solar WindS. 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

14. Incorporating Kinetic Effects into Global Models of the Solar WindS. 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...

15. Incorporating Kinetic Effects into Global Models of the Solar WindS. 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 R s β ≈ 0.003

16. Incorporating Kinetic Effects into Global Models of the Solar WindS. 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.