SOLAR WIND TURBULENCE;SOLAR WIND TURBULENCE;WAVE DISSIPATION AT ELECTRON WAVE DISSIPATION AT ELECTRON

SCALE WAVELENGTHSSCALE WAVELENGTHS

S. Peter GaryS. Peter Gary

Space Science InstituteSpace Science Institute

Boulder, COBoulder, CO

Meeting on Solar Wind TurbulenceMeeting on Solar Wind Turbulence

Kennebunkport, MEKennebunkport, ME

4-7 June 20134-7 June 2013

Magnetic Turbulence in the Solar Magnetic Turbulence in the Solar Wind: Sahraoui et al., PRL (2010)Wind: Sahraoui et al., PRL (2010)

Solar wind observations Solar wind observations from two Cluster from two Cluster magnetometers:magnetometers: FGM (f < 33 Hz) (blue curve)FGM (f < 33 Hz) (blue curve) STAFF-SC (1.5 < f <225 Hz) STAFF-SC (1.5 < f <225 Hz)

(green curve)(green curve)

Four regimes:Four regimes: Inertial with ~fInertial with ~f-5/3-5/3

““Transition rangeTransition range”” with ~f with ~f-4-4

““Dispersion rangeDispersion range”” withwith ~ ~ff-2.5-2.5

Electron Electron ““Dissipation rangeDissipation range”” with ~f with ~f-4-4

Magnetic Turbulence in the Solar Magnetic Turbulence in the Solar Wind: Narita et al., GRL (2011)Wind: Narita et al., GRL (2011)

Solar wind Solar wind observations from observations from four Cluster four Cluster spacecraft. spacecraft.

Fluctuations observed Fluctuations observed at both ω<Ωat both ω<Ωpp and and ω>Ωω>Ωpp in solar wind in solar wind frame.frame.

Most observations at Most observations at kk Bo.

Magnetic Turbulence in the Solar Magnetic Turbulence in the Solar Wind: Sahraoui et al., PRL (2010)Wind: Sahraoui et al., PRL (2010)

Solar wind Solar wind observations from observations from four Cluster four Cluster spacecraft. spacecraft.

Fluctuations only at Fluctuations only at ω<< Ωω<< Ωpp in solar wind in solar wind frame.frame.

Most observations at Most observations at kk Bo (θkB ≈ 90o).

Turbulence: Kolmogorov ScenarioTurbulence: Kolmogorov Scenario Turbulent energy is injected at very long wavelengths Turbulent energy is injected at very long wavelengths

and then cascades down toward short wavelengths and then cascades down toward short wavelengths along the along the ““inertial range.inertial range.””

At sufficiently short wavelengths, there is transfer of At sufficiently short wavelengths, there is transfer of energy in the energy in the ““dissipation rangedissipation range”” where fluctuations are where fluctuations are damped and the medium is heated.damped and the medium is heated.

But Plasmas Are Different…But Plasmas Are Different…

In neutral fluids, the Kolmogorov picture In neutral fluids, the Kolmogorov picture seems to work well; there are few normal seems to work well; there are few normal modes and collisions provide resistive and/or modes and collisions provide resistive and/or viscous dissipation.viscous dissipation.

But in magnetized collisionless plasmas, But in magnetized collisionless plasmas, there are many normal modes and several there are many normal modes and several different dissipation mechanisms.different dissipation mechanisms.

A Hypothesis for Short-A Hypothesis for Short-Wavelength Plasma TurbulenceWavelength Plasma Turbulence

The energy cascade from long to short wavelengths in The energy cascade from long to short wavelengths in plasmas remains a fundamentally nonlinear problem.plasmas remains a fundamentally nonlinear problem.

But at short wavelengths (f > 0.5 Hz in the solar wind near But at short wavelengths (f > 0.5 Hz in the solar wind near Earth), fluctuation amplitudes are relatively weak (|Earth), fluctuation amplitudes are relatively weak (| B| << B| << BBoo). ).

So we hypothesize that we can use linear theory to treat So we hypothesize that we can use linear theory to treat wave dispersion and wave-particle dissipation, and then wave dispersion and wave-particle dissipation, and then use this theory to explain and interpret the results from fully use this theory to explain and interpret the results from fully nonlinear simulations.nonlinear simulations.

Fundamental assumption: Homogeneous turbulence with Fundamental assumption: Homogeneous turbulence with constant background magnetic field and uniform plasma constant background magnetic field and uniform plasma parameters.parameters.

An Alternate Hypothesis for An Alternate Hypothesis for Plasma Turbulence DissipationPlasma Turbulence Dissipation The energy cascade from long to short wavelengths The energy cascade from long to short wavelengths

causes small-scale current sheets to form; these causes small-scale current sheets to form; these localized current sheets are the sites of strong localized current sheets are the sites of strong dissipation.dissipation.

Minping Wan has an invited talk on this topic later Minping Wan has an invited talk on this topic later today.today.

My concern will be linear dispersion and quasilinear My concern will be linear dispersion and quasilinear wave-particle dissipation in plasma turbulence.wave-particle dissipation in plasma turbulence.

Which Modes are Important?Which Modes are Important? Observations indicate that non-ideal physics in solar Observations indicate that non-ideal physics in solar

wind turbulence begins atwind turbulence begins at 1 ~ k1 ~ kc/ωc/ωpppp

And that most fluctuations propagate atAnd that most fluctuations propagate at kk Bo.

Linear theory predicts that the two modes most likely to satisfy these conditions are Kinetic Alfven waves and Magnetosonic-whistler modes.

Short-Wavelength Turbulence in the Short-Wavelength Turbulence in the Solar Wind: Two Basic ModesSolar Wind: Two Basic Modes

Kinetic Alfven waves Kinetic Alfven waves ω < Ωω < Ωpp

1 < k1 < kc/ωc/ωpppp < few < few ω ω ≅≅ k k|||| v vAA

Magnetosonic-whistler wavesMagnetosonic-whistler waves ΩΩpp < ω < Ω < ω < Ωee

(m(mee/m/mpp))1/21/2 < k c/ω < k c/ωpepe < few < few ω/Ωω/Ωee ~ kc/ω ~ kc/ωpppp + kk + kk|||| c c22/ω/ωpepe

22

Kinetic Alfven Wave Turbulence:Kinetic Alfven Wave Turbulence:Gyrokinetic SimulationsGyrokinetic Simulations

Gyrokinetic simulations use codes in Gyrokinetic simulations use codes in which the particle velocities are averaged which the particle velocities are averaged over a gyroperiod.over a gyroperiod.

Such codes are appropriate to model kinetic Such codes are appropriate to model kinetic Alfven waves (KAWs) which propagate at Alfven waves (KAWs) which propagate at ω < ω < ΩΩpp..

Howes et al. [2008, 2011], TenBarge and Howes et al. [2008, 2011], TenBarge and Howes [2013] and TenBarge et al. [2013] Howes [2013] and TenBarge et al. [2013] report detailed simulation studies of KAW report detailed simulation studies of KAW turbulence.turbulence.

Whistler turbulence:Whistler turbulence:Particle-in-cell SimulationsParticle-in-cell Simulations

Particle-in-cell (PIC) simulations treat the full three-dimensional Particle-in-cell (PIC) simulations treat the full three-dimensional velocity space properties of both electrons and ions.velocity space properties of both electrons and ions.

Such codes are appropriate to model whistler turbulence, which Such codes are appropriate to model whistler turbulence, which involve the full cyclotron motion of the electrons.involve the full cyclotron motion of the electrons.

PIC simulations require greater computational resources than PIC simulations require greater computational resources than gyrokinetic simulations, so whistler turbulence computations use gyrokinetic simulations, so whistler turbulence computations use smaller size boxes and run for shorter times than KAW smaller size boxes and run for shorter times than KAW simulations.simulations.

Saito et al. [2008, 2010] and Saito and Gary [2012] have done Saito et al. [2008, 2010] and Saito and Gary [2012] have done 2D PIC simulations of whistler turbulence, while Chang et al. 2D PIC simulations of whistler turbulence, while Chang et al. [2011; 2013] and Gary et al. [2012] have carried out fully 3D [2011; 2013] and Gary et al. [2012] have carried out fully 3D whistler turbulence PIC simulations.whistler turbulence PIC simulations.

Svidzinsky et al. [2009] carried out 2D PIC simulations of Svidzinsky et al. [2009] carried out 2D PIC simulations of magnetosonic-whistler turbulence. magnetosonic-whistler turbulence.

Magnetic Turbulence Simulation Spectra:Magnetic Turbulence Simulation Spectra:Wavenumber DependenceWavenumber Dependence

Kinetic Alfven turbulenceKinetic Alfven turbulence• Howes et al. [2011]Howes et al. [2011]• KAWs stronglyKAWs strongly• Spectral break at kρSpectral break at kρee~1~1

Whistler turbulenceWhistler turbulence Chang et al. [2011]Chang et al. [2011] ββee = 0.10, T = 0.10, Tee/T/Tpp=1=1

Spectral break at kc/ωSpectral break at kc/ωpepe~1~1

Magnetic Turbulence Simulation Spectra:Magnetic Turbulence Simulation Spectra:Wavevector AnisotropyWavevector Anisotropy

Kinetic Alfven turbulenceKinetic Alfven turbulence• Howes et al. [2011]Howes et al. [2011]• kk >> k >> k||||

Whistler turbulenceWhistler turbulence Chang et al. [2013a]Chang et al. [2013a] kk >> k >> k||||

Magnetic Turbulence Simulations:Magnetic Turbulence Simulations:DispersionDispersion

Kinetic Alfven turbulenceKinetic Alfven turbulence• Howes et al. [2008]Howes et al. [2008]

Whistler turbulenceWhistler turbulence Chang et al. [2013a]Chang et al. [2013a]

Magnetic Turbulence Simulations:Magnetic Turbulence Simulations:DissipationDissipation

Kinetic Alfven turbulenceKinetic Alfven turbulence Howes et al. [2011]Howes et al. [2011] Primary heating via Primary heating via

Landau resonance.Landau resonance. Only electrons heated Only electrons heated

at short wavelengths.at short wavelengths.

Whistler turbulenceWhistler turbulence Chang et al. [2013a]Chang et al. [2013a] Primary heating via Landau Primary heating via Landau

resonance.resonance. Only electrons heated.Only electrons heated. TT < T < T||||

Simulation SummariesSimulation Summaries Gyrokinetic simulations of KAW and PIC Gyrokinetic simulations of KAW and PIC

simulations of whistler turbulence both yield:simulations of whistler turbulence both yield: Forward cascade.Forward cascade. kk >> k >> k||||

Spectral breaks at electron scales (but different Spectral breaks at electron scales (but different scalings)scalings)

Consistency with linear dispersion theory.Consistency with linear dispersion theory. Parallel electron heating via Landau resonance.Parallel electron heating via Landau resonance.

Which Modes are More Which Modes are More Important?Important?

KAW School: Kinetic Alfven turbulence does KAW School: Kinetic Alfven turbulence does it all, cascading turbulent energy from the it all, cascading turbulent energy from the inertial range down to electron dissipation.inertial range down to electron dissipation.

Magnetosonic-whistler School: Magnetosonic Magnetosonic-whistler School: Magnetosonic turbulence weaker than Alfvenic turbulence at turbulence weaker than Alfvenic turbulence at inertial range, but nevertheless cascades inertial range, but nevertheless cascades down to short wavelengths where whistlers down to short wavelengths where whistlers dominate and heat electrons.dominate and heat electrons.

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

Questions in the Homogeneous Questions in the Homogeneous Turbulence ScenarioTurbulence Scenario

Are KAWs alone sufficient to describe Are KAWs alone sufficient to describe short-wavelength turbulence in the solar short-wavelength turbulence in the solar wind, or do magnetosonic-whistler wind, or do magnetosonic-whistler modes contribute?modes contribute?

Can Landau damping from either type Can Landau damping from either type of turbulence describe solar wind of turbulence describe solar wind electron heating?electron heating?

Beyond Homogeneous Turbulence: Beyond Homogeneous Turbulence: Karimabadi et al. [2013]Karimabadi et al. [2013]

Very large PIC simulations at Very large PIC simulations at β=0.1 with fluid-like β=0.1 with fluid-like instabilities cascading down to instabilities cascading down to electron scales.electron scales.

Panel (a): At ion gyroscales, Panel (a): At ion gyroscales, turbulence exhibits both Alfven turbulence exhibits both Alfven (A) modes and magnetosonic (A) modes and magnetosonic (M) waves.(M) waves.

Panel (b): Magnetic Panel (b): Magnetic Compressibility.Compressibility. CC||||(A) ~ 0 and C(A) ~ 0 and C||||(M) ~ 1. (M) ~ 1.

Beyond Homogeneous Turbulence: Beyond Homogeneous Turbulence: Karimabadi et al. [2013]Karimabadi et al. [2013]

Electrons are preferentially Electrons are preferentially heated in the directions parallel heated in the directions parallel and anti-parallel to the and anti-parallel to the background magnetic field. background magnetic field.

Parallel electron heating is Parallel electron heating is consistent with bothconsistent with both Landau damping of waves andLandau damping of waves and EE|||| generated by reconnection. generated by reconnection.

Analytic estimate: Current sheet Analytic estimate: Current sheet heating ~100 times larger than heating ~100 times larger than that due to Kinetic Alfven wave that due to Kinetic Alfven wave heating.heating.

Beyond Homogeneous Turbulence: Beyond Homogeneous Turbulence: TenBarge and Howes [2013]TenBarge and Howes [2013]

Gyrokinetic simulations at Gyrokinetic simulations at ββii=1 =1 form small-scale current sheets.form small-scale current sheets.

Black solid line: simulated Black solid line: simulated electron heating.electron heating.

Blue dashed line: Predicted Blue dashed line: Predicted electron heating by Landau electron heating by Landau damping.damping.

Red dashed line: Electron Red dashed line: Electron heating predicted by collisional heating predicted by collisional resistivity.resistivity.

Landau damping sufficient to Landau damping sufficient to account for electron heating in account for electron heating in simulation.simulation.

Beyond Homogeneous Turbulence: Beyond Homogeneous Turbulence: Chang et al. [2013b]Chang et al. [2013b]

Small box 3D PIC Small box 3D PIC simulations of whistler simulations of whistler turbulence.turbulence.

Electron-scale current Electron-scale current sheets form.sheets form.

At βAt βee<<1, linear damping <<1, linear damping

(dashed) << total dissipation (dashed) << total dissipation (solid).(solid).

At βAt βee=1, linear damping =1, linear damping

(dashed) ~ total dissipation (dashed) ~ total dissipation (solid).(solid).

Conclusions: Electron Conclusions: Electron DissipationDissipation

Linear electron damping/Total electron Linear electron damping/Total electron dissipation depends upon:dissipation depends upon: Kinetic Alfven waves vs. Whistler modesKinetic Alfven waves vs. Whistler modes Value of βValue of βee

Size of simulation boxSize of simulation box More simulations needed to quantify the More simulations needed to quantify the

dissipation mechanisms.dissipation mechanisms.