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
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)
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Four regimes:
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Inertial with ~f-5/3
“Transition range” with ~f-4
“Dispersion range” with ~f-2.5
Electron “Dissipation
range” with ~f-4
Magnetic Turbulence in the Solar
Wind: Narita et al., GRL (2011)
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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.
Magnetic Turbulence in the Solar
Wind: Sahraoui et al., PRL (2010)
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Solar wind
observations from
four Cluster
spacecraft.
Fluctuations only at
ω<< Ωp in solar wind
frame.
Most observations at
k  Bo (θkB ≈ 90o).
Turbulence: Kolmogorov Scenario
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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.
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.
A Hypothesis for ShortWavelength Plasma Turbulence
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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.
An Alternate Hypothesis for
Plasma Turbulence Dissipation
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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.
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.
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
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.
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Whistler turbulence:
Particle-in-cell Simulations
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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.
Magnetic Turbulence Simulation Spectra:
Wavenumber Dependence
Kinetic Alfven turbulence
•
•
•
Howes et al. [2011]
KAWs strongly
Spectral break at kρe~1
Whistler turbulence
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Chang et al. [2011]
βe = 0.10, Te/Tp=1
Spectral break at kc/ωpe~1
Magnetic Turbulence Simulation Spectra:
Wavevector Anisotropy
Kinetic Alfven turbulence
•
•
Howes et al. [2011]
k >> k||
Whistler turbulence
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Chang et al. [2013a]
k >> k||
Magnetic Turbulence Simulations:
Dispersion
Kinetic Alfven turbulence
•
Howes et al. [2008]
Whistler turbulence
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Chang et al. [2013a]
Magnetic Turbulence Simulations:
Dissipation
Kinetic Alfven turbulence
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Howes et al. [2011]
Primary heating via
Landau resonance.
Only electrons heated
at short wavelengths.
Whistler turbulence
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Chang et al. [2013a]
Primary heating via Landau
resonance.
Only electrons heated.
T < T||
Simulation Summaries
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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.
Which Modes are More
Important?
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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.
Shaikh & Zank, MNRAS, 400,1881 (2009)
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?
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Beyond Homogeneous Turbulence:
Karimabadi et al. [2013]
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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.
Beyond Homogeneous Turbulence:
Karimabadi et al. [2013]
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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.
Beyond Homogeneous Turbulence:
TenBarge and Howes [2013]
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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.
Beyond Homogeneous Turbulence:
Chang et al. [2013b]
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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).
Conclusions: Electron
Dissipation

Linear electron damping/Total electron
dissipation depends upon:
 Kinetic Alfven waves vs. Whistler modes
 Value of βe
 Size of simulation box
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More simulations needed to quantify the
dissipation mechanisms.