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S. R. Cranmer 1 , B. D. G. Chandran 2 , and A. A. van Ballegooijen 1

Tools for Predicting the Rates of Turbulent Heating for Protons, Electrons, & Heavy Ions in the Solar Wind. S. R. Cranmer 1 , B. D. G. Chandran 2 , and A. A. van Ballegooijen 1 (1) Harvard-Smithsonian CfA , (2) UNH. The Sun- heliosphere plasma system. The Sun- heliosphere plasma system.

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S. R. Cranmer 1 , B. D. G. Chandran 2 , and A. A. van Ballegooijen 1

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  1. Tools for Predicting the Rates of Turbulent Heating for Protons, Electrons, & Heavy Ions in the Solar Wind S. R. Cranmer1, B. D. G. Chandran2, and A. A. van Ballegooijen1 (1) Harvard-Smithsonian CfA, (2) UNH

  2. The Sun-heliosphere plasma system

  3. The Sun-heliosphere plasma system In situ: UV spectroscopy: O+6 O+5 electrons protons B

  4. Anisotropic MHD turbulence • Can MHD turbulence explain the presence of perpendicular ion heating? Maybe not! k ? Energy input k

  5. Anisotropic MHD turbulence • Can MHD turbulence explain the presence of perpendicular ion heating? Maybe not! • 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 Energy input k

  6. Anisotropic MHD turbulence • Can MHD turbulence explain the presence of perpendicular ion heating? Maybe not! • 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 ion cyclotron waves Ωp/VA kinetic Alfvén waves • In a low-β plasma, cyclotron waves heat ions & protons when they damp, but kinetic Alfvén waves are Landau-damped, heating electrons. Energy input k Ωp/cs

  7. Multi-mode coupling? • Fast-mode waves propagate – and cascade – more isotropically than Alfvén waves. • Chandran (2005) suggested that Alfvén and fast-mode waves may share energy via nonlinear couplings (AAF, AFF). If coupling is strong enough, some high-frequency fast-mode wave energy may feed back to the Alfvén modes → ion cyclotron! We model the wave transport → cascade → coupling → heating, in fast solar wind. • First, we solve radial transport equations for the energy densities (Um) of the individual Alfvén, fast, and slow mode fluctuations. (Jacques 1977) Damping rate: • turb. cascade • visc/cond/Ohm • For the Alfvén waves, Qm depends on: • Wave reflection:Z+ ≠ Z– (Chandran & Hollweg 2009) • Turb. correlation length L (obeys its own transport eqn.)

  8. Alfvén, fast, & slow mode waves in fast wind • We compute how the A, F, S modes perturb velocity, magnetic field, & density: • Free parameters: lower boundary conditions on Um & normalization for corr. length.

  9. Alfvén, fast, & slow mode waves in fast wind • Caveat: changing correlation length (L ~ 1/kouter) changes collisional damping a lot: • Our standard model for fast-mode waves is a representative example, not a definitive prediction! L at r = Rs: Earlier estimates: 75 km (CvB07) 300 km (CvB05) 300 km 200 km 130 km 100 km • It’s unlikely for Sun-generated slow-mode waves to survive to large heights, so we ignore them for remainder of this work (see, however, Howes et al. 2011). 50 km 30 km

  10. Model cascade + Alfvén/fast-mode coupling • Turbulent cascade modeled as time-steady advection/diffusion in wavenumber space. • Dissipation from KAW Landau damping (A) and transit-time damping (F) included. • Coupling between A & F modes treated with Chandran (2005) weak turb. timescale. Pure Alfvén mode: Alfvén mode with AAF/AFF coupling:

  11. Preliminary coupling results • We computed heating rates for protons & electrons from Vlasov-Maxwell dispersion. Fast-mode wave power varied up & down from the standard model . . . Helios & Ulysses

  12. Preferential heavy ion heating • UV spectroscopy provides constraints on Qion for O+5 ions in the corona . . . SUMER (Landi & Cranmer 2009); UVCS (Cranmer et al. 1999)

  13. Conclusions • Advances in MHD turbulence theory continue to help improve our understanding about kinetic particle heating in the corona and solar wind. • Our coupling mechanism is only one possibility: see SH43C-1974 (stochastic KAWs), SH43C-1967 (EMIC instability), SH53B-2036 (transit time damping), etc. • However, we still do not have complete enough observational constraintsto be able to choose between competing theories. For more information:http://www.cfa.harvard.edu/~scranmer/

  14. Extra slides . . .

  15. CPI is a large-aperture ultraviolet coronagraph spectrometer that has been proposed to be deployed on the International Space Station (ISS). • The primary goal of CPI is to identify and characterize the physical processes that heat and accelerate the plasma in the fast and slow solar wind. • CPI follows on from the discoveries of UVCS/SOHO, and has unprecedented sensitivity, a wavelength range extending from 25.7 to 126 nm, higher temporal resolution, and the capability to measure line profiles of He II, N V, Ne VII, Ne VIII, Si VIII, S IX, Ar VIII, Ca IX, and Fe X, never before seen in coronal holes above 1.3 solar radii. See white paper at: http://arXiv.org/abs/1104.3817 • 2011 September 29: NASA selected CPI as an Explorer Mission of Opportunity project to undergo an 11-month Phase A concept study.

  16. Mirror motions select height • UVCS “rolls” independently of spacecraft • 2 UV channels: • 1 white-light polarimetry channel LYA (120–135 nm) OVI (95–120 nm + 2nd ord.) The UVCS instrument on SOHO • 1979–1995: Rocket flights and Shuttle-deployed Spartan 201 laid groundwork. • 1996–present: The Ultraviolet Coronagraph Spectrometer (UVCS) measures plasma properties of coronal protons, ions, and electrons between 1.5 and 10 solar radii. • Combines “occultation” with spectroscopy to reveal the solar wind acceleration region! slit field of view:

  17. On-disk profiles: T = 1–3 million K Off-limb profiles: T > 200 million K ! UVCS results: solar minimum (1996-1997) • The Ultraviolet Coronagraph Spectrometer (UVCS) on SOHO measures plasma properties of coronal protons, ions, and electrons between 1.5 and 10 solar radii. • In June 1996, the first measurements of heavy ion (e.g., O+5) line emission in the extended corona revealed surprisingly wide line profiles . . .

  18. 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) θ k k Goldreich &Sridhar (1995) electron heating proton & ion heating

  19. Nonlinear mode coupling? • There is observational evidence for compressive (non-Alfvén) waves, too . . . (e.g., Krishna Prasad et al. 2011) Can Alfvénwaves couple with fast-mode wavesenough to feed back energy into the high-freq Alfvén waves? Chandran (2005) said maybe...

  20. Alfvén waves: from photosphere to heliosphere • Cranmer & van Ballegooijen (2005) assembled together much of the existing data on Alfvénic fluctuations: Hinode/SOT SUMER/SOHO G-band bright points UVCS/SOHO Helios & Ulysses Undamped (WKB) waves Damped (non-WKB) waves

  21. A turbulence-driven solar wind? • The measured wave dissipation is consistent with the required coronal heating! • 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. Z– Z+ Z– (e.g., Matthaeus et al. 1999) • Cranmer et al. (2007) explored the wave/turbulence paradigm with self-consistent 1D models, and found a wide range of agreement with observations. Ulysses 1994-1995

  22. Cranmer et al. (2007): other results Wang & Sheeley (1990) ACE/SWEPAM ACE/SWEPAM Ulysses SWICS Ulysses SWICS Helios (0.3-0.5 AU)

  23. Proton & ion energization (in situ) Wind @ 1 AU (Collier et al. 1996) ACE @ 1 AU (Berger et al. 2011) Helios @ 0.3–1 AU (Marsch 1991) B

  24. Alfven wave’s oscillating E and B fields ion’s Larmor motion around radial B-field Wave-particle interactions • Parallel-propagating ion cyclotron waves (10–10,000 Hz in the corona) have been suggested as a natural energy source . . . instabilities dissipation lower qi/mi faster diffusion (e.g., Cranmer 2001)

  25. Can turbulence preferentially heat ions? If turbulent cascade doesn’t generate the “right” kinds of waves directly, the question remains:How are the ions heated and accelerated? • When turbulence cascades to small perpendicular scales, the tight shearing motions may be able to generate ion cyclotron waves (Markovskii et al. 2006). • Dissipation-scale current sheets may preferentially spin up ions (Dmitruk et al. 2004; Lehe et al. 2009). • If MHD turbulence exists for both Alfvén and fast-mode waves, the two types of waves can nonlinearly couple with one another to produce high-frequency ion cyclotron waves (Chandran2005; Cranmer et al. 2012). • If nanoflare-like reconnection events in the low corona are frequent enough, they may fill the extended corona with electron beams that would become unstable and produce ion cyclotron waves (Markovskii 2007). • If kinetic Alfvén waves reach large enough amplitudes, they can damp via stochastic wave-particle interactions and heat ions (Voitenko & Goossens 2006; Wu & Yang 2007; Chandran 2010).

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