Turbulence in the Solar Atmosphere: Nature, Evolution and Impact

W. H. MatthaeusBartol 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 coronaSOHO spacecraft

UV spectrograph: EIT 340 A White 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 K @ 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, 2002Courtesy 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

IsotropicKolmogorovexponent

Anisotropic

Ion inertial scale

Solar Wind Density Spectra

“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

Athlons @ 1 GB/node– SAMSON2 128 x 1.6 GHz

Althons @1 GB/node– Wulfie 16 1.5 GHz

Athlons @ 512 MB/node

SAMSON

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

2D NS turbulence, Re=14,000, visualization of vorticity

t=1 t=21

t=52t=92

t=212t=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 ExperimentCothran, 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

Tnonlinear (k) < TAlfven (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, 1986Axford 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 profilesComparison 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

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Phenomenological model for radial evolution of SW turbulence

• Transport equations for turbulence energy Z2, 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, 1999Smith et al, JGR 2001Isenberg 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, 2002

• 2D axisymmetric heliosphere• Current sheet• 100 AU boundaries• Specified galactic spectrum• Turbulence properties transported outwards from 0.5 AU• Theoretical diffusion coefficients

Bartol/PotchModulation 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