Solar Wind: Low-frequency Turbulence in the Anisotropic Plasma
Namig Dzhalilov Shamakhy Astrophysical Observatory, Azerbaijan
1 A g e n d a
• Global structure of the heliosphere - general views • Solar wind measurements • The solar wind as a turbulence laboratory • MHD - Wave instability theory • Conclusions
2 3 The solar corona • Hot rarefied atmosphere above visible surface • Plasma beta <<1 in corona • magnetic field dominates
• Closed magnetic field: plasma trapped
• Open magnetic field: plasma can expand into interplanetary space
4 Eclipse: RED 1.1 106 K Iron X‐XI (RED) GREEN 2 106 K Iron XIII‐XIV (GREEN) This eclipse image shows the magnetic topology of the corona.
5 There is a clear separation of the high and low latitude solar wind.
6 This SOHO extreme ultraviolet (EIT) and scattered visible light (LASCO) composite image shows the outward streaming solar corona forming the supersonic solar wind 7 Expansion of the upper corona
• Corona is very hot • Pressure is higher than ambient interstellar medium • Expands into interplanetary space (Parker, 1958): solar wind
• Carves a cavity in interstellar medium: heliosphere
• Nearly radial flow • Accelerates to full speed by ~20 solar radii SoHO coronagraph (LASCO) Artificial eclipse
8 9 What is the solar wind?
• Collisionless, magnetised plasma • Continual, but variable, outflow from Sun’s corona • Blows a cavity in interstellar medium: heliosphere • Carries magnetic field, waves and turbulence from Sun’s corona • At edge of heliosphere, merges with interstellar medium • Interacts with planets and other bodies • Supersonic (super‐Alfvénic, …) • Hot: >105 K • Rarefied: few per cm3 at Earth • Complex due to solar variability, solar rotation, and in situ processes • Variable on all measured scales, from sub‐second centuries 10 What does the solar wind look like?
• Very rarefied • Can’t usually see it • Near‐Sun solar wind is visible during eclipses
11 12 Aurora
13 Magnetic Storms, 10‐11 Sept 2018
14 Cosmic Missions
1959 Luna‐1 ‐ ilk dəfə bu Sover süni peykində G küləyinin sürəti ölçüldü 1961 Venera 1 1962 Mariner 2 – Veneraya uçuş 1965 Venera 2 1972 Pioner 10 1973 Pioner 11 1973 Mariner 10 – Merkuri səfəri => 85 R 1976 HELİOS => 0.29 a.e. = 64 R 1977 Voyager 1, Voyager 2 1990 SOHO (Solar and Heliospheric Observatory) 1990 Ulysses GK yüksək en dairələrindən asılılığını tədqiq etdi. 1997 ACE (Advanced Composition Explorer) 2008 STEREO 2012 Messenger 2015 Bepi‐Columbo 2018 SPP (Solar Probe Plus) => 8.5 R 15 16 Significant spacecrafts Wind, ACE (present) • Near‐Earth (L1). Good, modern instrumentation Helios (1975‐1984?) • Closest approach to the Sun (0.29 AU, 63 solar radii) Ulysses (1990‐2006) • Only measurements at high latitudes Voyager 1 &2 , Pioneer 10 & 11 (mid‐1970’s, some still operating) • Only outer heliosphere measurements (80+AU)
we are here
17 18 19 Spacecraft particle measurements Measure: • Bulk distribution function, for ions and electrons Calculate: Moments of distribution function: velocity, temperature, density, etc.
• Particle composition (protons, helium, oxygen, etc.) • Ion charge states • Time variations at sub- gyroperiod scales
20 Spacecraft magnetic and electric field measurements • Measure magnetic and electric field from DC up to ~Hz, as time series • Measure higher frequencies (can be up to MHz) using spectra
Spacecraft measurements are difficult: • Very low fluxes and fields • Spacecraft contamination • Instrument effects • Low power and mass • Telemetry constraints
21 22 23 24 Histogram showing hourly average solar wind speeds measured by the spacecraft ACE (green) and Ulysses (blue). The vertical dashed black and red lines show typical slow and fast wind velocities respectively. We have only considered Ulysses measurements from when te spacecraft was less than 2.5 AU from the Sun. The distributions from the two spacecraft are different because they probed the solar wind at different latitudes. The orbit of ACE is in the equatorial plane, and therefore ACE measured mostly the slow component of the solar wind. The orbit of Ulysses is almost perpendicular to the equatorial plane, and therefore Ulysses measured both the slow and fast components of the solar wind.
25 26 Composition of the solar wind
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27 28 Global structure of the solar wind
• Source in the corona • Relation to coronal structure • Effect of solar rotation • Solar cycle dependence • Transient events • Interaction with the interstellar medium
29 Magnetic field: the Parker spiral
• Solar rotation drags out solar wind magnetic field into Archimedian spiral • Predicted by Gene Parker • Parker spiral
• Winding angle depends on wind speed, but: • ~45º at Earth • ~90º by 10 AU
Magnetic field is frozen in plasma! 30 IMF Sector Structure The heliospheric current sheet is the surface where the polarity of the Sun’s magnetic field changes sign. This field extends throu‐ ghout the Sun's equatorial plane in the heliosphere. A small electrical current flows within the sheet, about 10−10 A/m². The thickness of the current sheet is about 10,000 km near the orbit of the Earth. In
Out
31 The heliospheric current sheet, the largest coherent structure in the solar system, is a wavy sheet, resembling a ballerina skirt, due to the fact that the Sun’s magnetic dipole is tilted by different amounts, depending on the phase of the solar cycle, from its rotation axis. 32 Corotating Interaction Regions
33 Corotating Interaction Regions
34 The heliosphere Cosmic rays Heliopause
• Solar wind blows bubble in interstellar medium • Probably around 100 AU from Sun at Solar the nose wind Interstellar medium • Cosmic rays enter heliosphere: motion controlled by turbulent magnetic field Termination shock
35 The Heliosphere
36 Interstellar bowshocks • Shocks also form between stellar winds and interstellar medium • General shape is probably similar to the Sun’s bow shock NASA and The Hubble Heritage Team (STScI/AURA)
37 Pickup Ions can heat the Solar Wind?
38 The magnetosphere • Interaction of solar wind with Earth’s magnetic field • Bowshock: high Mach number shock • Magnetosheath: shocked solar wind plasma • Magnetosphere: very low beta plasma
Good: Many spacecraft Bad: High data rate Very complicated
39 40 Solar Wind Flow Near Sun
41 Temperature Gradients R < 1 AU
In the range 0.3 < R < 1.0 AU, Helios observations demonstrate the following: For V < 300 km/s, T ~ R ‐1.3 0.13 SW Adiabatic expansion ‐1.2 0.09 ‐4/3 300 < VSW < 400 km/s, T ~ R yields T ~ R . ‐1.0 0.10 400 < VSW < 500 km/s, T ~ R Low speed wind ‐0.8 0.10 500 < VSW < 600 km/s, T ~ R expands without in ‐0.8 0.09 situ heating!? 600 < VSW < 700 km/s, T ~ R ‐0.8 0.17 High speed wind is 700 < VSW < 800 km/s, T ~ R heated as it expands. Why is this? It seems distinct from the high‐latitude observations. We can look to explain this through theory and link it to observations of the dissipation range and inferred spectral cascade rates.
42 Turbulence
43 Importance of waves and turbulence
Energetic particle transport • Controls cosmic rays throughout the solar system Effect on the Earth • Can trigger reconnection, substorms, aurorae, … Understanding solar processes • Signature of coronal heating, etc. Application to astrophysical plasmas • Turbulence is pervasive Turbulence as a universal phenomenon • Comparison with hydrodynamics
44 Solar wind as a turbulence laboratory
• Characteristics – Collisionless plasma – Variety of parameters in different locations – Contains turbulence, waves, energetic particles • Measurements – In situ spacecraft data – Magnetic and electric fields – Bulk plasma: density, velocity, temperature, … – Full distribution functions – Energetic particles
45 Solar wind as a plasma experiment
46 47 48 Three months of solar wind data Ulysses: 4.5 AU • Field and particle measurements • MHD on these scales
• Variable speed, density, magnetic field, …
• Not random: presence of large scale structures • 30‐day repeats
49 Typical conditions at 0.3 AU
• Closest measurements to date • Before stream‐stream interactions are important • Highest density in slow wind
Density and temperature anticorrelated
Magnetic field ~0º from radial
50 Typical conditions at 1.0 AU
• Stream‐stream interactions more important • Shocks beginning to form
Density and temperature correlated: compression at velocity increase
Magnetic field ~45º from radial: Parker spiral
51 Stream dependence: cross helicity
• Wavelets: measure time and frequency dependence of waves
Fast wind Positive cross helicity: anti‐sunward Alfvén waves
Sharp transition To mixed sense waves
Slow wind Mixed sense, but very variable
52 53 54 55 56 57 Dominance of outward‐propagating waves
Speed • Solar wind accelerates as it Solar wind speed leaves the corona • Alfvén speed decreases as field magnitude drops Critical point • Alfvén critical point: equal speed (~10‐20 solar radii) Alfvén speed • Above critical point, all waves carried outward
Therefore, • Outward‐propagating low Distance from Sun frequency waves generated in corona!
58 59 60 61 Problem turbulence anisotropy
62 63 64 The turbulent solar wind
f ‐1 turbulence
waves f ‐5/3
Power spectrum • Broadband • Fluctuations on all • Low frequencies: f ‐1 measured scales • High frequencies: f ‐5/3
65 Large scale variations in power levels
• Power in high speed wind, low and high latitudes
• Ulysses agrees well with Helios • Data taken 25+ years apart
• Increasing scatter in Helios reflects stream‐stream interactions
66 Results: Fundamental observations of waves and turbulence
Alfvén waves • Waves of solar origin
Active turbulent cascade • Not just remnant fluctuations from corona
Intermittency • Similar high order statistics to hydrodynamics
Field‐aligned anisotropy • Fundamental difference to hydrodynamics
67 Theory: Turbulent Flow Dynamics
Vortices of dissimilar size lead to convection rather than destruction.
Interacting vortices lead to distortion, stretching, and destruction (spawning).
68 Kolmogorov’s First Hypothesis of Similarity Argues the spectrum can depend only on theAs phrased by Frisch (1995): scale size and the rate of local interaction! This means that the inertial and dissipation ranges can“At very large, but not infinite Reynolds numbers, all be represented as : the small‐scale statistical properties are uniquely and E(k) 2/3k 5/3Fk universally determined by the scale L, the mean whereenergy dissipation rate F k is a universal, and the viscosity function. .” ‐ FKolmogorov (1941)k CK 1.6 in the inertial range. (Reprinted in Proc. R. Soc. London A, 434, 9, 1991.) The value CK 1.6 has been confirmed by experiment : Sreenivasan, K.R., Phys. Fluids, 7(11), 2778 (1995) It also means that ~ L /V. 69 Kraichnan Theory
Iroshnikov (1964) and Kraichnan (1965) argue that in MHD wave propagation is more important that turbulent eddy interaction. L The timescale for this is . L VA This results in a different prediction for the turbulent spectrum : 1/ 2 -3/2 E(k) AIK VA k and a different rate of energy interaction : energy V2 V2V L L A timescale L/VA L
70 Verification of Kolmogorov Prediction
Inertial range spectrum ~ ‐5/3
Grant, Stewart, and Moilliet, J. Fluid Mech., 12, 241‐268, 1962.
Spectral steepening with dissipation
71 Turbulent Cascade
72 Summary of Wind Turbulence Large scales are dictated by sun. Geometry velocity‐ordered… Large‐scale energy source… …evolving toward 2D geometry… …feeds an energy‐ with compression conserving cascade… …plasma …until fluid approx. kinetic physics.
Magnetic + Velocity Power breaks down.
1 / (Few hours) 0.2 Hz 73 Motivation • Solar wind fluctuations are observed to exhibit an f‐5/3 spectral form in the range from a few hours to a few seconds. Figure (right) shows the magnetic power spectrum over 2+ decades in frequency and steepening to form the dissipation range.
The ‐5/3 spectrum extends down to Inertial range Ion inertial scale about 10‐5 Hz. spectrum ~ 5/3 Because the wind speed is so great, we believe that temporal Spectral steepening with dissipation measurements (Hz) are equivalent to spatial measurements (km‐1):
k = kVSW/2 and k=2/. 74 What is Kolmogorov Saying? Large‐scale fluctuations (eddy’s, waves, shears, ejecta, shocks, whatever) contain a lot of energy, but direct dissipation of that energy is slow (except maybe shocks). The turbulent inertial range cascade converts energy of the large‐scale objects into smaller scales until dissipation becomes important. In this manner, the large‐scale “structure” of the flow can heat the thermal particles of the fluid. This occurs within the fluid description! Does this apply to the solar wind and other space plasmas? It appears that dissipation in the solar wind occurs outside the fluid description, which complicates and changes the problem. 75 A New View??? • Coleman, Phys. Rev. • Coleman, Astrophys. J., Lett., 17, 207 (1966) 153, 371 (1968)
Fluctuations in the wind Fluctuations arise in situ and IMF are presumed as result of large‐scale to be waves, most likely interplanetary sources Alfven waves, that are such as wind shear and remnant signatures evolve non‐linearly in a propagating out from manner analogous to the solar corona. traditional hydro‐ dynamic turbulence.
76 Need to understand
Why do we always see the same spectral form ‐ EVERYWHERE?
Why/How does the spectrum change over scales?
How do we tap the wave energy to create heat?
77 Why is it difficult?
• Complications: – MHD is not hydrodynamics! – …but it contains hydrodynamics! – There are multiple time scales. – There are wave dynamics. • The mean field provides a direction of special importance! – The spectra are not isotropic.
• Can we build a theory of MHD turbulence that brings ideas from hydrodynamics into the problem? • Dissipation is NOT provided by the fluid equation! – Dissipation marks the breakdown of the fluid approximation. – Going to need kinetic physics for dissipation!?!
78 Weak turbulence: mixture of waves with random phases
Theory of Waves and Instabilities in an Anisotropic Collisionless Plasmas
79 Anisotropic plasmas refer to situations where the velocity distribution functions of the various particle species are non isotropic (in particular non Maxwellian). Such a regime requires Coulomb collisions to be sufficiently weak.
Many astrophysical plasmas are magnetized and weakly or even almost non collisional.
Characterized by: Collision frequency << cyclotron frequency Larmor radius << mean free path
Examples include: • Galaxy cluster plasmas Schekochihin et al. ApJ 629, 139 (2005) • Solar wind Marsch , Space Sc. Rev. 172, 22, (2012) • Planet magnetospheres Blanc et al. Space Sci. Rev. 116, 227 (2005)
80 In situ observations in the solar wind:
‐ Velocity distribution functions exhibit large departures from isotropic (Maxwellian) distribution functions:
‐Different parallel and perpendicular temperatures with respect to the ambient magnetic field.
‐ The proton distribution function often exhibit a core and a magnetic field‐aligned beam with • a number density of the order of tenths of the core density • the beam/core relative velocity of the order of the local Alfvén velocity (Marsch et al., JGR 87, 35, 1982).
81 82 Main Motivation
‐ Pressure anisotropy is a source of free energy (energy that can be transformed into work).
‐ The system will tend to relax or to reduce this anisotropy via collisions or, if they are too weak to act efficiently, by developing instabilities which push the system towards equilibrium.
83 84 85 Waves and Instabilities in MHD scales
86 Isotropic collisional MHD equations
87 The kinetic equations Boltzmann‐Vlasov
fa u f 1 F e E 1 [u B] f Q( f ) t a ma a a c a v a a
+ Maxwell equations for the electromagnetic field
fa(u,r,t) – distribution function of a‐sort particles – not Maxwellian! 1/ 2 1 2 3/ 2 n 6 l.h.s. O(1) r.h.s.=Q(f) O(g) g 3 (4 e ) 3/ 2 10 n rD T The number of particles in a plasma sphere
with a Debye radius of rD . Therefore collisions can be neglected,
Q = 0 ‐ collisionless plasma
88 Integrated functions = moments
They allow a fluid description of the plasma motion.
n(r,t) f du ‐‐ plasma density 1 v(r,t) u f du ‐‐ fluid velocity of plasma n 1 2 2 ‐‐ anisotropic plasma p p m( u u ) f du pressure || 2 || S 1 mu 2 u f du ‐‐ heat flux ||, 2 ||, 16 moments of the distribution function: density (1) + velocity vector (3) + pressure (or temperature) (2) + stress tensor (4) + two vectors of heat fluxes (6) = 16 89 CGL-MHD equations on the base of the 13-moments transport equations Chew, Goldberger & Low 1956, Proc.Roy.Soc. London A,236,112
d d dt div V 0, d t t V
dV B2 1 dt ( p 8 ) 4 (B)B g ( p p )[ h divh (h )h] h(h )( p p ), || || 2 d p||B dt 3 0, two adiabatic Heat fluxes are ignored! invariants d p dt B 0, dB B dt B div V (B)V 0, divB 0, h B 90 MHD equations on the base of the 16‐moments transport equations
91 Proton anisotropy
Slow wind Fast wind
92 Electron anisotropy
Slow wind Fast wind
93 Stream interaction regions
Figure 7: A sketch of a stream interaction region. Left: Looking down on the ecliptic plane. Magn field lines within fast (slow) wind, shown in red (blue), become aligned with the stream interface reverse (forward) wave. Right: a view from Earth. The magnetic axis, M, and therefore the wind s belts, are inclined to the rotation axis, R. The point in the heliosphere at which fast wind is able t up to the slow wind ahead of it is the stream interface (SI), which forms a spiral front in the helio shown as the black‐outlined curved surface. In the frame of reference of the SI, both fast and slo flow toward the SI. Fast (slow) wind, shown by the red (blue) arrow, is slowed (accelerated) and d along the SI in the direction counter to (along) solar rotation. Right panel adapted from Pizzo (194 9 Shear instability growing rate in CIR
95 The main problem of the physics of the heliosphere has not been solved yet: how are particles of the solar wind heated and accelerated?
Great hope for anisotropic MHD !
T H A N K S !
96