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

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 Overview

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

Activity in the solar chromosphere and corona SOHO spacecraft UV spectrograph: EIT 340 AWhite light coronagraph: LASCO C3

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

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

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

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 Artist conception

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 Belcher and Davis, JGR, 1972 Mariner 2 data

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

Turbulence: Navier Stokes Equations

Turbulence: nonlinearity and cascade

Standard powerlaw cascade picture

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 Mean flow Instantaneous flow VanDyke, An Album of Fluid Motion

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

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 1 GB/node –SAMSON2 128 x 1.6 GHz GB/node –Wulfie GHz 512 MB/node SAMSON

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

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

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…)

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

Two-dimensional turbulence and random-convection-driven reconnection

Low frequency Nearly Incompressible Quasi-2D cascade Dominant nonlinear activity involves k’s such that T nonlinear (k) < T Alfven (k) Transfer in perp direction, mainly k perp >> k par

Turbulence in the heliosphere

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

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

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

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

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

Reduced MHD simulation Dmitruk and Matthaeus, 2002

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

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

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

Phenomenological model for radial evolution of SW turbulence Transport equations for turbulence energy Z 2, energy-containing scale  and temperature T effect of large scale wind shear  V ~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

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

Ab Initio theory of the solar modulation of galactic cosmic rays

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

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

Bartol/Potch Modulation results Parhi et al, 2002 Excellent spectrum at 1 AU Good radial gradient Latitudinal gradient: “working on it”

Scattering mean free paths of solar energetic particles

Scattering of solar energetic particles (SEP) 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 WIND magnetic field spectrum Current work by Droege, 2002 Bieber et al, 1994

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

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

Conclusions: MHD Plasma Turbulence 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 Consequences for upcoming NASA mission - Magnetospheric Multiscale (MMS) - L1 Constellation - Solar Probe - ……

Acceleration of test particles by turbulent electric field  =  Alfven /  gyro Particles start with v=0 Distribution after 0.5  Alfven Two powerlaws