Colloquium presented at the University of New Hampshire, November 21, 2002

1. Turbulence in the Solar Atmosphere: Nature, Evolution and ImpactW. H. MatthaeusBartol Research Institute, University of Delaware Collaborators: P. Dmitruk, S. Oughton, L. Milano, D. Mullan, G. Zank, R. Leamon, C Smith, D. Montgomery Colloquium presented at the University of New Hampshire, November 21, 2002

2. Overview • Corona, solar wind and heliospheric turbulence • Background in Turbulence theory • Distinctive features of MHD and plasmas • Applications • Coronal heating • Solar wind transport and heating • Solar modulation of galactic cosmic rays • Solar energetic particles

3. Comet tails and the solar wind Second (ion) tail suggests solar wind exists (Biermann, 1951 ) Hale-Bopp

4. Activity in the solar chromosphere and coronaSOHO spacecraft UV spectrograph: EIT 340 A White light coronagraph: LASCO C3

5. Fine scale activity in the corona FE IX/X lines, TRACE Drawings from Coronagraphs (Loucif and Koutchmy, 1989)

6. Large scale features of the solar wind • Plasma outflow, spiral magnetic field • High and low speed streams • North south distorted magnetic dipole • Wavy, equatorial current sheet

7. Large scale features of the Solar Wind: Ulysses • High latitude • Fast • Hot • steady • Comes from coronal holes • Low latitude • slow • “cooler” (40,000 K @ 1 AU) • nonsteady • Comes from streamer belt McComas et al, GRL, 1995

8. Artist conception Largest scale features of the Solar Wind: • Boundaries of the heliosphere: interaction of the solar wind with the interstellar medium. • Nonlinear flows/ turbulence provide essential interactions that establish global structure NAS SSP Survey Report, 2002 Courtesy JPL

9. The solar wind is turbulent • Fluctuations in velocity and magnetic field are irregular, not “reproducible,” broad-band in space and time • Indications of turbulence properties and wave-like properties Mariner 2 data Belcher and Davis, JGR, 1972

10. Broadband self-similar spectra are a signature of cascade “Powerlaws everywhere” Interstellar medium: Armstrong et al • Solar wind • Corona • Diffuse ISM • Geophysical flows SW at 2.8 AU: Matthaeus and Goldstein Tidal channel: Grant, Stewart and Moilliet Coronal scintillation results (Harmon and Coles)

11. Turbulence: Navier Stokes Equations

12. Turbulence: nonlinearity and cascade

13. Standard powerlaw cascade picture

14. VanDyke, An Album of Fluid Motion Mean flow and fluctuations • In turbulence there can be great differences between mean state and fluctuating state • Example: Flow around sphere at R = 15,000 Instantaneous flow Mean flow

15. Why turbulence is important • transport (diffusion, mixing…) • heating • charged particle scattering • charged particle acceleration • cross scale couplings

16. Turbulence computations and parallel computing • Substantial computational resources are required • Special thanks to Pablo Dmitruk, Sean Oughton and Ron Ghosh (and the NSF!) • Three Beowulf clusters • SAMSON 132 x 1 Ghz Athlons @ 1 GB/node • SAMSON2 128 x 1.6 GHz Althons @1 GB/node • Wulfie 16 1.5 GHz Athlons @ 512 MB/node SAMSON

17. Example: Decaying (Unforced) 2D hydrodynamic Turbulence • Re = 14,000 • 512*512 spectral method • Visualize vorticity • “Isolated vortices” • Vortex sheets • Merger/collision vortices Dmitruk and Matthaeus, 2002

18. 2D NS turbulence, Re=14,000, visualization of vorticity Montgomery et al, 1990 t=1 t=21 t=92 t=52 t=332 t=212

19. Magnetohydrodynamic (MHD) turbulence • velocity, magnetic field, density • Hydro plus Lorentz force, and magnetic induction • Good for plasmas at low frequency, long wavelength • Can include kinetic corrections (e.g., Hall effect…)

20. Distinctive features of MHD • MHD Waves, esp. Alfven waves • Dynamo action • Anisotropy: Magnetic field imposes a preferred direction • Magnetic reconnection Swarthmore Spheromak Experiment Cothran, Brown, Landeman and Matthaeus, 2002

22. Two-dimensional turbulence and random-convection-driven reconnection

23. Low frequency Nearly Incompressible Quasi-2D cascade • Dominant nonlinear activity involves k’s such that Tnonlinear(k) < TAlfven (k) • Transfer in perp direction, mainly • k perp >> k par

24. Turbulence in the heliosphere

25. Heliospheric turbulence: Applications • Coronal heating • Solar wind heating • Solar modulation of cosmic rays • Spatial diffusion of solar energetic particles • turbulence and “space weather”

26. Heating the lower corona using a strong turbulent MHD cascade driven by low frequency Alfven waves

27. Network and furnace • photospheric motions (~100 sec flows and magnetic reconnection in the network) • provide fluctuations that can power coronal heating Axford and McKenzie, 1997 Dowdy et al, 1986

28. Turbulence model of coronal heating • Interacting waves drive low frequency MHD cascade • Energy transfer to small transverse scales produces heating • Powered by low frequency upwards traveling Alfven waves • Only counterpropagating or nonpropagating fluctuations can interact • Reflection is essential

29. Sustainment of a wave driven cascade • Two factors are crucial: • reflection (source of counterstreaming waves) • Excitation of nonpropagating structures, which do not “empty” in a crossing time

30. Reduced MHD simulation Dmitruk and Matthaeus, 2002

31. Comparison of three simulations Comparison of three simulations with different density profiles Density profile determines heating profile Extended Heating per unit mass Heating/volume is ~exponentially confined

32. Heating the solar wind in the outer heliosphere (> 1 AU)

33. Something is heating the solar wind in the outer heliosphere (> 1 AU) Voyager proton temperatures Richardson et al, GRL, 1995

34. Phenomenological model for radial evolution of SW turbulence • Transport equations for turbulence energy Z2, energy-containing scale l, and temperature T • effect of large scale wind shear DV ~100 km/sec • wave generation by pickup ions associated with interstellar neutral gas • Anisotropic decay and heating phenomenology Matthaeus et al, PRL, 1995; Smith et al, JGR, 2001; thanks to Phil Isenberg

35. Solar Wind Heating • Perpendicular MHD cascade/transport theory accounts for radial evolution from 1 AU to >50 AU • Proton temperature • Fluctuation level • Correlation scale(?) ADIABATIC Matthaeus et al, PRL, 1999 Smith et al, JGR 2001 Isenberg et al, 2002

36. Ab Initio theory of the solar modulation of galactic cosmic rays

37. Structure of modulation theory • Adopt model for solar wind average velocity, density and magnetic field. • Adopt a 2 component turbulence model • Solve transport equations to get turbulence energy and correlation scale throughout heliosphere • Use theory of parallel and perpendicular diffusion coefficients  these depend on turbulence properties • Solve Parker transport equation (convection, diffusion and expansion) for source spectrum of galactic cosmic rays at heliospheric boundary • Compare with observations

38. Cosmic ray intensities throughout the heliosphere • 2D axisymmetric heliosphere • Current sheet • 100 AU boundaries • Specified galactic spectrum • Turbulence properties transported outwards from 0.5 AU • Theoretical diffusion coefficients Parhi et al, 2002

39. Bartol/PotchModulation results Parhi et al, 2002 • Excellent spectrum at 1 AU • Good radial gradient • Latitudinal gradient: “working on it”

40. Scattering mean free paths of solar energetic particles

41. Scattering of solar energetic particles (SEP) Current work by Droege, 2002 WIND magnetic field spectrum • Parallel scattering theory was considered “hopeless” as recently as 15 years ago…However… • Diffusion coefficients measured from time profiles of SEPs • Turbulence properties measured by same spacecraft • Use theory of particle scattering in dynamical turbulence AND 2-component turbulence model with dissipation range • COMPUTE mean free path for SEPs that agrees well with observations Bieber et al, 1994

42. Possible geospace effects and space weather • Geo-effectiveness of interplanetary activity may depend on more than just polarity of IMF and the solar wind speed and pressure • Possibilities: • Shear and turbulence geometry • Gradient of turbulence properties such as Reynolds stress • Turbulent drag on magnetosphere • Nonlinear dynamics of Coronal Mass Ejections

43. L1-constellation • Multi spacecraft plasma explorer proposed 1980 • Various future heliospheric multi S/C mission proposed • L1-Constellation possible NOW using WIND, ACE, Genesis and SOHO (and Triana if it is launched) What is the three dimensional nature of plasma turbulence, shocks, discontinuities, and other structures in the near Earth Solar Wind?  How does turbulence interact with interplanetary structures and inhomogeneities?  How do factors related to turbulence affect Sun-Earth Connection physics? Presented to the 2002 NASA Roadmap meeting by J. Borovsky and W. Matthaeus

44. A natural laboratory for study of turbulence as a fundamental physical process A prototype for astrophysical turbulence Mediates cross scale couplings Enhances transport and heating Couples energetic particles to the plasma Couplings to Geospace environment Coronal heating Solar wind evolution Modulation Solar energetic particles Conclusions: MHD Plasma Turbulence • Consequences for upcoming NASA mission • - Magnetospheric Multiscale (MMS) • - L1 Constellation • - Solar Probe • - ……

45. Acceleration of test particles by turbulent electric field a = tAlfven/tgyro • Particles start • with v=0 • Distribution after • 0.5 tAlfven • Two powerlaws