1. NSO Summer School Lecture 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. V SW is not Function of R Richardson et al., GRL, 22, 325, 1995. Density multiplied by R 2.

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. Solar Wind Properties At 1 AU: –V SW ~ 300-800 km/s –N p ~ 10 p + /cm 3 –T p ~ 10 5 K –|B| ~ 6 nT –  BR ~ 45  At 100 AU: –V SW ~ 450 km/s –N p ~ 10  3 p + /cm 3 –T p ~ 10 4 K –|B| ~ 0.06 nT –  BR ~ 90  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. V SW ~ 300 to 800 km/s flowing away from sun (averages ~1,000,000 miles/hr) Stays ~ constant as it flows from the sun. T p ~ 4 x 10 4 to 2 x 10 5 K (V p th ~ 50 km/s ~ V s ) N p ~ 3 to 10 p + /cm 3 Decreases ~ 1/R 2 from sun. |B| ~ 3 to 10 nT (B Wash.DC = 5.7 x 10 4 nT) Decreases ~ 1/R from sun. Energy Output of the Sun Solar output in light: The solar constant is 135.3 mWatts/cm 2 which corresponds to a radiant solar energy of ~1.4 GigaWatts/km 2 (1.4 x 10 9 Watts/km 2 ). Multiplying by area of sphere 1 AU = 1.49 x 10 8 km in radius (4  R 2 ) gives solar output of light energy at 3.9 x 10 26 Watts. For comparison: 10 protons/cm 3 traveling at 450 km/s has an energy flux density of… (1/2) (M P N P V SW ) V SW 2 = 7.6 x 10 2 Watts/km 2 Integrating over a 1 AU sphere, the sun’s energy production in the solar wind is 2.1 x 10 20 Watts.

11. Solar Wind Composition About 96% is p + and about 4% is He ++. The rest is: Detailed composition measurements attempt to refine physics of 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 V A = (B 0 2 /4  N P m P ) 1/2 ~ constant  P = eB 0 /m P c ~ |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 Charged particles do not cross magnetic field lines! They can travel along B lines, but not across. B0B0 The magnetic force is at right angles to the particle motion and the magnetic field direction.  + k || v p =  n 

21. 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. f  5/3

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

24. 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 Vlasov Equation (Collisionless Boltzman’s Equation) } } Maxwell’s Equations governing Electro- Magnetic Fields Charge density, currents, etc. are computed from the distribution of particles for all species

25. Newborn Interstellar Pickup Ions V SW 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.

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: 1.Examine global structure of heliosphere 2.Examine properties of fluctuations 3.Compute wave solutions to MHD 4.Ask: Can waves heat the solar wind? Nope! They can’t without something more. 5.Begin to re-examine properties of fluctuations

28. 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. Belcher & Davis, J. Geophys. Res., 76, 3534 (1971).

29. Magnetic Fluctuation Spectrum Matthaeus et al., Phys. Res. Lett., 48, 1256 (1982). 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

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

31. Low-Frequency MHD Waves

32. Propagation and Dissipation B0B0 VV  V  B < 0  propagation along B 0

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 Slides in 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. 3b. Alfven and Fast-Mode Waves 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)

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. 5c. Multi-D H C =  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  /  E V +E B  so that  1   C  +1 Milano et al., Phys. Rev. Lett., 93(15), 155005 (2004).

43. 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. Dasso et al., ApJ, 635, L181-184 (2005). Slow wind is 2DFast wind is 1D

44. 5e. Decay of H C (Cross-Correlation) H C  V  B  /  V 2 +  B 2  Strong correlations evident at 1 AU disappear by ~ 4 AU. Roberts et al., J. Geophys. Res., 92(10), 11021, 1987.

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. 6a. A New View 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.

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

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 2 nd -order interaction of linear waves. –Oppositely propagating low-frequency waves interact to produce a “daughter” wave propagating obliquely in a 3 rd direction. Requires that transfer rates be slow compared with wave periods. Traditionally give suspect predictions (in my humble opinion)

51. Hydrodynamic Turbulence: Laminar vs. Turbulent Flow Interacting vortices lead to distortion, stretching, and destruction (spawning).

52. One Example of Turbulence Contributed by Pablo Dimitric of the Bartol Research Inst.

53. Navier-Stokes Equation Mass DensityFluid PressureDissipation of Energy Incompressibility (constant mass) Convective derivative (time variability following the flow)

54. Energy Conservation 0 00 Energy Conserving

55. Wave Vector Dynamics Dissipation at large wave numbers

56. MHD Equations The Navier-Stokes equation represents a system where the nonlinear terms move energy without changing the total energy and viscosity dissipates energy at the smallest scales. Can the MHD equations do something comparable?

57. Over the Next Two Days: In Tuesday’s seminar we will explore one very powerful formulation for measuring the rate of energy cascade in the spectrum. In Wednesday’s class we will continue to explore the concepts of MHD turbulence.

58. Extra Slides

59. 1 AU Conditions Solar wind speed, V SW, varies from 250 to 800 km/s. (R Earth = 6371 km, an 8 second transit at high wind speed.) At least 2 transients have been observed at 2000 km/s at 1 AU! Proton density varies, but averages about 10 p + /cm 3. We are unable to achieve these densities on the surface of the Earth. Proton temperature averages about 10 5 K. (V th ~ 50 km/s for ions.) Magnetic clouds are colder (1/10’th), high speed streams are colder… Magnetic field averages 6 to 8 nT and 45° from radial direction. (B Earth = 5.7 x 10 4 nT at Washington DC.) Can be just about anything at any time. Have reached 55 nT during ACE era and << 1 nT. Heavy ions (He ++, He +, Fe ?+, C ?+, O ?+, etc.) provide clues to origins.

60. 1c. N P Varies as R  2 A1A1 A 2 = A 1 (R 2 /R 1 ) 2

61. 1d. Adiabatic Expansion Vasquez et al., J. Geophys. Res., 112, A07101 (2007).

62. 1e. Radial IMF Flux of IMF through closed surfaces surrounding the sun is constant.

63. 1f. Azimuthal IMF Note error in Kallenrode book!

64. 1g. IMF Intensity and Direction

65. Solar Wind Structure (Magnetic) Expanding solar wind draws sun’s magnetic field outward as sun rotates underneath to create a spiral interplanetary magnetic field (IMF). IMF winding results from a “connect-the- dots” approach to plasma elements moving outward and sun rotating.

66. Magnetohydrodynamics (MHD) There is a mathematical formalism that (we believe) describes the low-frequency fluctuations in the solar wind. It is derived from a combination of Maxwell’s equations for E&M and statistical mechanics. It attempts to present a fluid description for a plasma without particle collisions. These equations break down when spatial (temporal) scales become smaller (faster) than the orbit of a proton. There is a formal description to plasmas under these conditions.

67. Waves vs. Turbulence and more… Can we understand reproducible observations in basic terms? What are the universal processes of space physics? What can we assume of unmeasured and partially measured physics? Can we move toward a predictive understanding that gets dynamics right, or just qualities in general?

68. …and Why? Because waves are a relatively static phenomenon. –The propagate, but are reluctant to give up their energy. Turbulence is an inherently dynamic phenomenon. –Energy moves through the spectrum continuously and defines EVERYTHING!

69. Temperature Gradients R < 1 AU In the range 0.3 < R < 1.0 AU, Helios observations demonstrate the following: For V SW < 300 km/s, T ~ R -1.3  0.13 300 < V SW < 400 km/s, T ~ R -1.2  0.09 400 < V SW < 500 km/s, T ~ R -1.0  0.10 500 < V SW < 600 km/s, T ~ R -0.8  0.10 600 < V SW < 700 km/s, T ~ R -0.8  0.09 700 < V SW < 800 km/s, T ~ R -0.8  0.17 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. Adiabatic expansion yields T ~ R -4/3. Low speed wind expands without in situ heating!? High speed wind is heated as it expands.

70. Can Waves Heat the Solar Wind? In the range 0.3 < R < 1.0 AU, Helios observations demonstrate the following: For V SW < 300 km/s, T ~ R -1.3  0.13 300 < V SW < 400 km/s, T ~ R -1.2  0.09 400 < V SW < 500 km/s, T ~ R -1.0  0.10 500 < V SW < 600 km/s, T ~ R -0.8  0.10 600 < V SW < 700 km/s, T ~ R -0.8  0.09 700 < V SW < 800 km/s, T ~ R -0.8  0.17 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. Adiabatic expansion yields T ~ R -4/3. Low speed wind expands without in situ heating!? High speed wind is heated as it expands. The slow wind continues to accelerate from 0.3 to 1 AU (due to in situ heating?), which complicated the analysis for years! The temperature of all solar wind intervals 0.3 to 1 AU varies as R  0.9 ! All low-latitude winds are heated inside 1 AU! Heating rate at 1 AU averages ~ 3 x 10 3 Joules/kg-s. See Vasquez, J. Geophys. Res., 112, 2007.

71. Before There Were Spacecraft… There were comet tails. Something blows the tails of comets away from sun. Light pressure cannot explain it. Sometimes the tails become disconnected.

72. 1 AU Conditions (Near Earth) Solar wind speed, V SW, varies from 250 to 800 km/s. (R Earth = 6371 km, an 8 second transit at high wind speed.) At least 2 transients have been observed at 2000 km/s at 1 AU! Proton density varies, but averages about 10 p + /cm 3. We are unable to achieve these densities on the surface of the Earth. Proton temperature averages about 10 5 K. (V th ~ 50 km/s for ions.) Magnetic clouds are colder (1/10’th). Interplanetary magnetic field averages 6 to 8 nT and 45° from radial direction. (B Earth = 5.7 x 10 4 nT at Boulder, Colorado.) IMF can be just about anything at any time. Have reached 55 nT during ACE era and << 1 nT. Heavy ions (He ++, He +, Fe ?+, C ?+, O ?+, etc.) provide clues to origins.

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

74. Solar Wind Variability While we will see there is all sorts of variability from one hour to the next, there is also a systematic variability tied to the solar cycle. This reflects the Sun’s changing state with high-speed wind sources moving to new latitudes and multiple wind sources interacting. This variability propagates into the outer heliosphere, forms merged regions of plasma that alter the propagation of galactic cosmic rays Earthward, and effects the acceleration of energetic particles within the heliosphere.

75. Solar Energetic Particles Solar flares on Bastille Day 2000 marked the eruption of coronal magnetic fields and associated plasma. This ejection resulted in the acceleration of ions and electrons via mechanisms still under study. ACE observed the energetic particles arrived at Earth several days ahead of the ejecta. Orbiting spacecraft were damaged or destroyed. Loss of electrical power was threatened. Astronauts were endangered.

76. Low-Frequency Waves Alfven waves: –Transverse magnetic and velocity fluctuations –No density compressions –   k  B 0 /  (4  ) Fast Mode waves: –Some field-aligned V and B fluctuations –Some compression for off-axis propagation –   k B 0 /  (4  )

77. Solar Wind Flow Near Sun

78. Magnetohydrodynamics (MHD) There is a mathematical formalism that (we believe) describes the low-frequency fluctuations in the solar wind. It is derived from a combination of Maxwell’s equations for E&M and statistical mechanics. It attempts to present a fluid description for a plasma without particle collisions. These equations break down when spatial (temporal) scales become smaller (faster) than the orbit of a proton. There is a formal description to plasmas under these conditions.

79. A Model to Think About: All that energy has to go someplace! –All energy goes into heat. Will MHD turbulence (in analogy with hydrodynamic turbulence) converts large-scale energy into small-scale energy? Will combination of processes (mostly kinetic physics) converts collective motions into heat? –Cyclotron damping, Landau damping, current sheet formation, etc….

80. Shock Acceleration

81. Day 49, 1999 Upstream Waves “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 and ESP. 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. f  5/3

82. Proton Distribution Functions Marsch, Phys. Inner Heliosphere 2, Chapter 8 (1991) “Among the most typical features are…pronounced total temperature anisotropies with T P  > T P|| and anisotropic cores in high-speed [winds] and… T P|| > T P  and isotropic cores in low-speed [winds].”