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![Page 1: Turbulence in the Solar Atmosphere: Nature, Evolution and Impact W. H. Matthaeus Bartol Research Institute, University of Delaware Colloquium presented.](https://reader030.fdocuments.net/reader030/viewer/2022020213/5a4d1acf7f8b9ab059970b7c/html5/thumbnails/1.jpg)
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
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• 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
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Comet tails and the solar wind
Second (ion) tail suggests solar wind exists (Biermann, 1951 )
Hale-Bopp
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Activity in the solar chromosphere and coronaSOHO spacecraft
UV spectrograph: EIT 340 A White light coronagraph: LASCO C3
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Fine scale activity in the corona
Drawings from Coronagraphs (Loucif and Koutchmy, 1989)
FE IX/X lines, TRACE
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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
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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
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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
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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
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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
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Turbulence: Navier Stokes Equations
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Turbulence: nonlinearity and cascade
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Standard powerlaw cascade picture
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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
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Why turbulence is important
• transport (diffusion, mixing…)• heating• charged particle scattering• charged particle acceleration• cross scale couplings
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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
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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
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2D NS turbulence, Re=14,000, visualization of vorticity
t=1 t=21
t=52t=92
t=212t=332
Montgomery et al, 1990
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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…)
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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
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Two-dimensional turbulence and random-convection-driven reconnection
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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
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Turbulence in the heliosphere
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Heliospheric turbulence: Applications
• Coronal heating• Solar wind heating• Solar modulation of cosmic rays• Spatial diffusion of solar energetic particles• turbulence and “space weather”
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Heating the lower corona using a strong turbulent MHD cascade driven by low
frequency Alfven waves
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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
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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
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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
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Reduced MHD
simulation
Dmitruk and Matthaeus, 2002
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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
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Heating the solar wind in the outer heliosphere (> 1 AU)
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Something is heating the solar wind in the outer heliosphere (> 1 AU)
Voyager proton temperatures
Richardson et al, GRL, 1995
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2
32
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31
34
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ZUk
mrT
drdT
EZU
ZUr
Cdrd
UEZ
UZ
rA
drdZ
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PI
PI
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
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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
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Ab Initio theory of the solar modulation of galactic cosmic
rays
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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
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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
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Bartol/PotchModulation results
Parhi et al, 2002
•Excellent spectrum at 1 AU•Good radial gradient•Latitudinal gradient: “working on it”
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Scattering mean free paths of solar energetic particles
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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
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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
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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
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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 - ……
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Acceleration of test particles by turbulent electric field
=Alfven/gyro
•Particles start with v=0•Distribution after 0.5 Alfven
•Two powerlaws