SOLAR WIND TURBULENCE; WAVE DISSIPATION AT ELECTRON SCALE WAVELENGTHS

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) • Solar wind observations from two Cluster magnetometers: • FGM (f < 33 Hz) (blue curve) • STAFF-SC (1.5 < f <225 Hz) (green curve) • 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) • Solar wind observations from four Cluster spacecraft. • Fluctuations observed at both ω<Ωp and ω>Ωp in solar wind frame. • Most observations at k Bo.

4. Magnetic Turbulence in the Solar Wind: Sahraoui et al., PRL (2010) • Solar wind observations from four Cluster spacecraft. • Fluctuations only at ω<< Ωp in solar wind frame. • Most observations at k Bo (θkB ≈ 90o).

5. Turbulence: Kolmogorov Scenario • Turbulent energy is injected at very long wavelengths and then cascades down toward short wavelengths along the “inertial range.” • 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… • In neutral fluids, the Kolmogorov picture seems to work well; there are few normal modes and collisions provide resistive and/or viscous dissipation. • But in magnetized collisionless plasmas, there are many normal modes and several different dissipation mechanisms.

7. A Hypothesis for Short-Wavelength Plasma Turbulence • The energy cascade from long to short wavelengths in plasmas remains a fundamentally nonlinear problem. • But at short wavelengths (f > 0.5 Hz in the solar wind near Earth), fluctuation amplitudes are relatively weak (| B| << Bo). • 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. • Fundamental assumption: Homogeneous turbulence with constant background magnetic field and uniform plasma parameters.

8. An Alternate Hypothesis for Plasma Turbulence Dissipation • 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. • Minping Wan has an invited talk on this topic later today. • My concern will be linear dispersion and quasilinear wave-particle dissipation in plasma turbulence.

9. Which Modes are Important? • Observations indicate that non-ideal physics in solar wind turbulence begins at • 1 ~ kc/ωpp • And that most fluctuations propagate at • k Bo. • 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 • Kinetic Alfven waves • ω < Ωp • 1 < kc/ωpp < few • ω ≅ k|| vA • Magnetosonic-whistler waves • Ωp < ω < Ωe • (me/mp)1/2 < k c/ωpe < few • ω/Ωe ~ kc/ωpp + kk|| c2/ωpe2

11. Kinetic Alfven Wave Turbulence:Gyrokinetic Simulations • Gyrokinetic simulations use codes in which the particle velocities are averaged over a gyroperiod. • Such codes are appropriate to model kinetic Alfven waves (KAWs) which propagate at ω < Ωp. • 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 • Particle-in-cell (PIC) simulations treat the full three-dimensional velocity space properties of both electrons and ions. • Such codes are appropriate to model whistler turbulence, which involve the full cyclotron motion of the electrons. • 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. • 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. • Svidzinsky et al. [2009] carried out 2D PIC simulations of magnetosonic-whistler turbulence.

13. Magnetic Turbulence Simulation Spectra:Wavenumber Dependence Kinetic Alfven turbulence Whistler turbulence Chang et al. [2011] βe = 0.10, Te/Tp=1 Spectral break at kc/ωpe~1 • Howes et al. [2011] • KAWs strongly • Spectral break at kρe~1

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

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

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

17. Simulation Summaries • Gyrokinetic simulations of KAW and PIC simulations of whistler turbulence both yield: • Forward cascade. • 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? • KAW School: Kinetic Alfven turbulence does it all, cascading turbulent energy from the inertial range down to electron dissipation. • 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 • Are KAWs alone sufficient to describe short-wavelength turbulence in the solar wind, or do magnetosonic-whistler modes contribute? • Can Landau damping from either type of turbulence describe solar wind electron heating?

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

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

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

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

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