1. SOLAR WIND TURBULENCE; WAVE DISSIPATION AT ELECTRON SCALE WAVELENGTHS S. Peter Gary Space Science Institute Boulder, CO Meeting on Solar Wind Turbulence Kennebunkport, ME 4-7 June 2013

2. Magnetic Turbulence in the Solar Wind: Sahraoui et al., PRL (2010) n Solar wind observations from two Cluster magnetometers:  FGM (f < 33 Hz) (blue curve)  STAFF-SC (1.5 < f <225 Hz) (green curve) n Four regimes:  Inertial with ~f -5/3  “Transition range” with ~f -4  “Dispersion range” with ~ f -2.5  Electron “Dissipation range” with ~f -4

3. Magnetic Turbulence in the Solar Wind: Narita et al., GRL (2011) n Solar wind observations from four Cluster spacecraft. n Fluctuations observed at both ω Ω p in solar wind frame. n Most observations at k n Most observations at k  B o.

4. Magnetic Turbulence in the Solar Wind: Sahraoui et al., PRL (2010) n Solar wind observations from four Cluster spacecraft. n Fluctuations only at ω<< Ω p in solar wind frame. n Most observations at k n Most observations at k  B o (θ kB ≈ 90 o ).

5. Turbulence: Kolmogorov Scenario n Turbulent energy is injected at very long wavelengths and then cascades down toward short wavelengths along the “inertial range.” n At sufficiently short wavelengths, there is transfer of energy in the “dissipation range” where fluctuations are damped and the medium is heated.

6. But Plasmas Are Different… n In neutral fluids, the Kolmogorov picture seems to work well; there are few normal modes and collisions provide resistive and/or viscous dissipation. n But in magnetized collisionless plasmas, there are many normal modes and several different dissipation mechanisms.

7. A Hypothesis for Short- Wavelength Plasma Turbulence n The energy cascade from long to short wavelengths in plasmas remains a fundamentally nonlinear problem. n But at short wavelengths (f > 0.5 Hz in the solar wind near Earth), fluctuation amplitudes are relatively weak (|  B| 0.5 Hz in the solar wind near Earth), fluctuation amplitudes are relatively weak (|  B| << B o ). n So we hypothesize that we can use linear theory to treat wave dispersion and wave-particle dissipation, and then use this theory to explain and interpret the results from fully nonlinear simulations. n Fundamental assumption: Homogeneous turbulence with constant background magnetic field and uniform plasma parameters.

8. An Alternate Hypothesis for Plasma Turbulence Dissipation n The energy cascade from long to short wavelengths causes small-scale current sheets to form; these localized current sheets are the sites of strong dissipation. n Minping Wan has an invited talk on this topic later today. n My concern will be linear dispersion and quasilinear wave-particle dissipation in plasma turbulence.

9. Which Modes are Important? n Observations indicate that non-ideal physics in solar wind turbulence begins at  1 ~ k  c/ω pp n And that most fluctuations propagate at  k  k  B o. n n Linear theory predicts that the two modes most likely to satisfy these conditions are   Kinetic Alfven waves and   Magnetosonic-whistler modes.

10. Short-Wavelength Turbulence in the Solar Wind: Two Basic Modes n Kinetic Alfven waves  ω < Ω p  1 < k  c/ω pp < few  ω ≅ k || v A n Magnetosonic-whistler waves  Ω p < ω < Ω e  (m e /m p ) 1/2 < k c/ω pe < few  ω/Ω e ~ kc/ω pp + kk || c 2 /ω pe 2

11. Kinetic Alfven Wave Turbulence: Gyrokinetic Simulations n Gyrokinetic simulations use codes in which the particle velocities are averaged over a gyroperiod. n Such codes are appropriate to model kinetic Alfven waves (KAWs) which propagate at ω < Ω p. n Howes et al. [2008, 2011], TenBarge and Howes [2013] and TenBarge et al. [2013] report detailed simulation studies of KAW turbulence.

12. Whistler turbulence: Particle-in-cell Simulations n Particle-in-cell (PIC) simulations treat the full three-dimensional velocity space properties of both electrons and ions. n Such codes are appropriate to model whistler turbulence, which involve the full cyclotron motion of the electrons. n PIC simulations require greater computational resources than gyrokinetic simulations, so whistler turbulence computations use smaller size boxes and run for shorter times than KAW simulations. n Saito et al. [2008, 2010] and Saito and Gary [2012] have done 2D PIC simulations of whistler turbulence, while Chang et al. [2011; 2013] and Gary et al. [2012] have carried out fully 3D whistler turbulence PIC simulations. n Svidzinsky et al. [2009] carried out 2D PIC simulations of magnetosonic-whistler turbulence.

13. Magnetic Turbulence Simulation Spectra: Wavenumber Dependence Kinetic Alfven turbulence Howes et al. [2011] KAWs strongly Spectral break at kρ e ~1 Whistler turbulence n Chang et al. [2011] n β e = 0.10, T e /T p =1 n Spectral break at kc/ω pe ~1

14. Magnetic Turbulence Simulation Spectra: Wavevector Anisotropy Kinetic Alfven turbulence Howes et al. [2011] k  >> k || Whistler turbulence n Chang et al. [2013a] n k  >> k ||

15. Magnetic Turbulence Simulations: Dispersion Kinetic Alfven turbulence Howes et al. [2008] Whistler turbulence n Chang et al. [2013a]

16. Magnetic Turbulence Simulations: Dissipation Kinetic Alfven turbulence n Howes et al. [2011] n Primary heating via Landau resonance. n Only electrons heated at short wavelengths. Whistler turbulence n Chang et al. [2013a] n Primary heating via Landau resonance. n Only electrons heated. n T  < T ||

17. Simulation Summaries n Gyrokinetic simulations of KAW and PIC simulations of whistler turbulence both yield:  Forward cascade.  k >> k ||  k  >> k ||  Spectral breaks at electron scales (but different scalings)  Consistency with linear dispersion theory.  Parallel electron heating via Landau resonance.

18. Which Modes are More Important? n KAW School: Kinetic Alfven turbulence does it all, cascading turbulent energy from the inertial range down to electron dissipation. n Magnetosonic-whistler School: Magnetosonic turbulence weaker than Alfvenic turbulence at inertial range, but nevertheless cascades down to short wavelengths where whistlers dominate and heat electrons.

19. Shaikh & Zank, MNRAS, 400,1881 (2009)

20. Questions in the Homogeneous Turbulence Scenario n Are KAWs alone sufficient to describe short-wavelength turbulence in the solar wind, or do magnetosonic-whistler modes contribute? n Can Landau damping from either type of turbulence describe solar wind electron heating?

21. Beyond Homogeneous Turbulence: Karimabadi et al. [2013] n Very large PIC simulations at β=0.1 with fluid-like instabilities cascading down to electron scales. n Panel (a): At ion gyroscales, turbulence exhibits both Alfven (A) modes and magnetosonic (M) waves. n Panel (b): Magnetic Compressibility.  C || (A) ~ 0 and C || (M) ~ 1.

22. Beyond Homogeneous Turbulence: Karimabadi et al. [2013] n Electrons are preferentially heated in the directions parallel and anti-parallel to the background magnetic field. n Parallel electron heating is consistent with both  Landau damping of waves and  E || generated by reconnection. n Analytic estimate: Current sheet heating ~100 times larger than that due to Kinetic Alfven wave heating.

23. Beyond Homogeneous Turbulence: TenBarge and Howes [2013] n Gyrokinetic simulations at β i =1 form small-scale current sheets. n Black solid line: simulated electron heating. n Blue dashed line: Predicted electron heating by Landau damping. n Red dashed line: Electron heating predicted by collisional resistivity. n Landau damping sufficient to account for electron heating in simulation.

24. Beyond Homogeneous Turbulence: Chang et al. [2013b] n Small box 3D PIC simulations of whistler turbulence. n Electron-scale current sheets form. n At β e <<1, linear damping (dashed) << total dissipation (solid). n At β e =1, linear damping (dashed) ~ total dissipation (solid).

25. Conclusions: Electron Dissipation n Linear electron damping/Total electron dissipation depends upon:  Kinetic Alfven waves vs. Whistler modes  Value of β e  Size of simulation box n More simulations needed to quantify the dissipation mechanisms.