NSO Summer School Lecture 1: Solar Wind Structure and Waves

1. NSO Summer SchoolLecture 1:Solar Wind Structure and Waves Charles W. Smith Space Science Center University of New Hampshire Charles.Smith@unh.edu

2. Good References: • Space Physics – May-Britt Kallenrode, Springer 2001. (~ $70) • Turbulence -- Uriel Frisch, Cambridge University Press 1995. (~ $35 to $55) • Magnetohydrodynamic Turbulence – Dieter Biskamp, Cambridge 2003. (~ $110) • The Solar Wind as a Turbulence Laboratory -- Bruno and Carbone, on line @ Living Reviews in Solar Physics (free)

3. Coronal mass ejections are plasma eruptions from the sun that are fast-moving. They are predictable, but only approximately. Some are self-contained magnetic structures called magnetic clouds that are observed to be cold at 1 AU. Charge-state composition data strongly indicates they originate in hot electron environments. Overexpansion is largely responsible for observed temperature at 1 AU. In situ heating rate can be calculated from fluctuations.

4. Origin of the Solar Wind Model drawn from many remote sensing methods: Note rapid rise in temperature in so-called “transition region” around 2000 km about photosphere. Source of heat is not known, although widely speculated upon.

5. Solar Wind Acceleration Scatter plots of velocity as a function of distance for the emitted plasma puffs and solid line showing best fits to radial profile. These plots show the expected outflow that Solar Probe will encounter during its perihelion pass (Sheeley et al., 1997).

6. Heating the Solar Wind

7. VSW is not Function of R Density multiplied by R2. Richardson et al., GRL, 22, 325, 1995.

8. The Solar Wind Continues Flowing Outward, Away from the Sun • Studied by Pioneers 10 & 11 • Had enough power to function to 35 AU • Studied by Voyagers 1 & 2 • Still operating at ~100 AU • Recall crossing of termination region crossing • To a lesser degree: • Cassini, Galileo, and other planetary missions

9. At 1 AU: VSW ~ 300-800 km/s Np ~ 10 p+/cm3 Tp ~ 105 K |B| ~ 6 nT BR ~ 45 At 100 AU: VSW ~ 450 km/s Np ~ 103 p+/cm3 Tp ~ 104 K |B| ~ 0.06 nT BR ~ 90 Solar Wind Properties By 100 AU: Streams merge, gradients are smoothed, & few shocks remain, Fluctuations are reduced, but persist, Interstellar neutrals / pickup ions dominate pressure, Thermal composition is unchanged.

10. Energy Output of the Sun Solar output in light: The solar constant is 135.3 mWatts/cm2 which corresponds to a radiant solar energy of ~1.4 GigaWatts/km2 (1.4 x 109 Watts/km2). Multiplying by area of sphere 1 AU = 1.49 x 108 km in radius (4R2) gives solar output of light energy at 3.9 x 1026 Watts. For comparison: 10 protons/cm3 traveling at 450 km/s has an energy flux density of… (1/2) (MP NP VSW) VSW2 = 7.6 x 102 Watts/km2 Integrating over a 1 AU sphere, the sun’s energy production in the solar wind is 2.1 x 1020 Watts. VSW ~ 300 to 800 km/s flowing away from sun (averages ~1,000,000 miles/hr) Stays ~ constant as it flows from the sun. Tp ~ 4 x 104 to 2 x 105 K (Vpth ~ 50 km/s ~ Vs) Np ~ 3 to 10 p+/cm3 Decreases ~ 1/R2 from sun. |B| ~ 3 to 10 nT (BWash.DC = 5.7 x 104 nT) Decreases ~ 1/R from sun.

11. Solar Wind Composition • About 96% is p+ and about 4% is He++. • The rest is: Detailedcompositionmeasurementsattempt torefine physicsof acceleration.

12. Solar Activity 1992-1999 The Sun through the Eyes of SOHO SOHO Project Scientist Team

13. Global Structure Wind speed is independent of heliocentric distance. Density ~ R2 IMF wound in a spiral |B| ~ R2 inside 2 AU ~ R1 outside 2 AU VA = (B02/4NPmP)1/2 ~ constant P = eB0/mPc ~ |B|

14. Solar Wind Gradients Fast winds slam into slow winds creating “interaction regions” (corotating, merged, global, etc.). Magnetic fields can be sheared. Fluctuations are enhanced. Lots of dynamics!!!

15. These are Not Rare Events

16. Earth’s Magnetosphere

17. CME Interacting with Earth

18. Transient Arrival of Bastille Day 2000 Over a week of extensive solar activity 3 shocks and associated ejecta arrived at Earth. Each resulted in energetic particle enhancements to varying degrees. Each resulted in magneto-spheric storm activity to varying degrees.

19. Shocks

20. Particle Gyromotion & Resonance  + k||vp = n B0 Charged particles do not cross magnetic field lines! They can travel along B lines, but not across. The magneticforce is at right anglesto the particle motion andthe magnetic field direction.

21. f5/3 Analysis: Day 49 of 1999 • “Classic” upstream wave spectrum for older, well-developed event (as expected). • Broad spectrum of upstream waves. • Not much polarization. No real surprises here. Upstream spectrum from prior to the onset of the SEP. Power law form has no net polarization and there is a spectral break to form the dissipation range. This is a typical undisturbed solar wind interval.

22. Quasi-Parallel Diffuse ions Ion Foreshock Boundary Gyrophase Bunched Electrons I FAB Earth B Quasi-Perpendicular Energetic Particle Populations Upstream of the Earth’s Bow Shock Gyrotropic distribution Diffuse distribution Intermediate distribution Gyrophase-bunched Field-aligned beam Specularly reflected ions

24. } Maxwell’s Equations governing Electro-Magnetic Fields Vlasov Equation (Collisionless Boltzman’s Equation) } Charge density, currents, etc. are computed from the distribution of particles for all species Formalisms of Plasma Physics • We can build a mathematical formalism for the theory of freely-interacting charged particles • Start with Maxwell’s equations governing E&M • Add the Boltzman equation from statistical mechanics • Obtain the Maxwell-Vlasov equations of plasma physics • We can “simplify” this to a set of fluid equations • Magneto-fluid equations called the MHD equations • Generally applicable to low-frequency phenomena

25. Newborn Interstellar Pickup Ions Interstellar neutral enter the heliosphere at small speeds, are ionized either by charged particle collision or photo-ionization, are “picked up” by the solar wind & IMF, and convected back to termination region. In the process their circulation of the IMF provides “free energy” for exciting magnetic waves that can provide energy for heating the thermal plasma. VSW

26. Waves Due to Pickup Ions Traditional plasma theory suggests that wave spectra due to pickup ions will reach LARGE enhancements in the background power levels (left, Lee & Ip, 1987). They don’t! (below, Murphy et al., 1995) Wave growth is slow and turbulent processes overwhelm the plasma kinetics of wave excitation (for once).

27. We Could Do 5 Things Today: • Examine global structure of heliosphere • Examine properties of fluctuations • Compute wave solutions to MHD • Ask: Can waves heat the solar wind? • Nope! They can’t without something more. • Begin to re-examine properties of fluctuations

28. Belcher & Davis, J. Geophys. Res., 76, 3534 (1971). Properties of Fluctuations • Low-frequency fluctuations tend to be: • Transverse to the mean magnetic field. • Have low density compressions (/0~0.1). • Not generally well-correlated with fields. • Correlated B and V fluctuations. • Indicative of outward propagation. • Evolution of power consistent with WKB. • Reproducible power spectral form! • Varying intensity.

29. Magnetic Fluctuation Spectrum The spectrum of magnetic fluctuations follows a predictable and reproducible form (power law with index ~ 5/3). The magnetic helicity (polarization) is mixed. f5/3 Matthaeus et al., Phys. Res. Lett., 48, 1256 (1982).

30. Velocity Fluctuation Spectrum Podesta et al., J. Geophys. Res., 111, A10109 (2006).

31. Low-Frequency MHD Waves

32. Propagation and Dissipation B0 V VB < 0  propagation along B0

33. So, Life is Good! …or, is it?

34. Can Waves Heat the Solar Wind? Imagine that there is a spectrum of waves originating at the sun and propagating outward. As the wave gets further from the sun, the mean magnetic field decreases and the cyclotron resonance shifts to lower frequencies (larger scales). The spectrum of wave energy is slowly consumed from the high-frequency end. Schwartz et al., JGR, 86, 541 (1981)

35. Homework Problem: • Take the energy spectrum of solar wind fluctuations • Magnetic + Velocity • Compute the rate of P  0 as R  . • Compute the rate of energy input to the solar wind by damping the static spectrum. • What is the local heating rate? • How long before the entire inertial range energy is consumed?

36. Pickup Ions Heat the Solar Wind

37. Summary • The heliosphere is vast, structured, and containing a broad range of dynamics. • Filled with expanding, supersonic solar wind. • Transients and planetary interactions drive shocks and particle acceleration. • Interstellar neutrals / ions provide new dynamics. • Waves may explain (some of?) the fluctuations seen in the solar wind. • How can the velocity and magnetic spectra differ? • What happened to all that pickup ion wave energy? • We will challenge this claim.

38. Extra Slidesin No Particular Order

39. Homework Problem: • If you haven’t already, explore the MHD wave solutions that give Alfven and fast-mode waves in the fluid approximation. • Obtain dispersion relations, polarization, fluctuation directions. • If you haven’t already, review the kinetic theory descriptions of the same waves. • Obtain polarization and dissipation.

40. Alfven waves are: Noncompressive Transverse fluctuations Right-hand polarized Move energy parallel to mean field Decay via cyclotron damping on ions Decay via Landau resonance (ions & electrons) Fast-Mode Waves: Compressive for off-axis propagation Not transverse at off-axis propagation Left-hand polarized Move energy across the mean field for off-axis propagation Convert to whistler waves Decay via cyclotron damping on electrons Decay via Landau resonance (ions & electrons) 3b. Alfven and Fast-Mode Waves

41. 5b. Multi-D Correlation Fn. Combining analyses of many intervals, adding correlation functions according to mean field direction, can lead to an understanding (statistically):Matthaeus et al., J. Geophys. Res., 95, 20,673, 1990. Bieber et al., J. Geophys. Res., 101, 2511, 1996 showed the 2D component dominates.

42. Milano et al., Phys. Rev. Lett., 93(15), 155005 (2004). 5c. Multi-D HC = VB If there is a V and a B so that there is a VB, there must be sufficient energy to support VB. Define C  VB / EV+EB so that 1  C  +1

43. Slow wind is 2D Fast wind is 1D Dasso et al., ApJ, 635, L181-184 (2005). 5d. Breaking Apart the Maltese Cross Combining analyses of many intervals, adding correlation functions according to mean field direction, can lead to an understanding (statistically):Matthaeus et al., J. Geophys. Res., 95, 20,673, 1990. Bieber et al., J. Geophys. Res., 101, 2511, 1996 showed the 2D component dominates.

44. Roberts et al., J. Geophys. Res., 92(10), 11021, 1987. 5e. Decay of HC (Cross-Correlation) HCVB / V2+B2 Strong correlations evident at 1 AU disappear by ~ 4 AU.

45. Re-examine the Observations • Are the fluctuations really waves at all? • What is the orientation of k? • …and how did it get there? • Is VB  0 indication of propagation? • What happens when we add energy? • …where does it go? • …and how does it get there? • What about that spectrum?

46. Coleman, Phys. Rev. Lett., 17, 207 (1966) Fluctuations in the wind and IMF are presumed to be waves, most likely Alfven waves, that are remnant signatures propagating out from the solar corona. Coleman, Astrophys. J., 153, 371 (1968) Fluctuations arise in situ as result of large-scale interplanetary sources such as wind shear and evolve non-linearly in a manner analogous to traditional hydro-dynamic turbulence. 6a. A New View

47. Ion Inertial Scale Inertial range spectrum ~ 5/3 Inertial rangespectrum ~ -5/3 Spectral steepening with dissipation Grant, Stewart, and Moilliet, J. Fluid Mech., 12, 241-268, 1962. Spectral steepening with dissipation 6b. A New View f -1“energy containing range”  = V3/L f -5/3 “inertial range” If the inertial range is a pipeline, the dissipation range consumes the energy at the end of the process. Magnetic Power f -3“dissipation range” This is the essence of hydrodynamic turbulence applied to MHD! Few hours 0.5 Hz

48. 6c. A New View • 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!?!

49. What is Turbulence? It is the nonlinear evolution of the fluid away from its initial state and toward a self-determined state.

50. Weak Turbulence Theory • One view, popular in plasma theory, is that turbulence is just the 2nd-order interaction of linear waves. • Oppositely propagating low-frequency waves interact to produce a “daughter” wave propagating obliquely in a 3rd direction. • Requires that transfer rates be slow compared with wave periods. • Traditionally give suspect predictions (in my humble opinion)