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A REVIEW OF WHISTLER TURBULENCE BY THREE-DIMENSIONAL PIC
SIMULATIONSS. Peter Gary, Space Science Institute
Ouliang Chang, Oracle Corporation
R. Scott Hughes and Joseph WangUniversity of Southern
California
Queenstown, New Zealand9 February 2015
- A Viewpoint for Short-Wavelength Turbulence Short-wavelength
turbulence is fundamentally nonlinear and must be treated with
fully nonlinear techniques such as particle-in-cell simulations.At
short wavelengths, fluctuation amplitudes are relatively weak (|
B|
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Short Wavelength Turbulence in the Solar Wind: Sahraoui et al.
(2010)Cascade of long wavelengths to dissipation at short
wavelengths.Inertial range: 10-4 Hz < f < 0.5 HzKinetic range
(aka Dissipation range):0.5 Hz < f < 100s HzKinetic Alfven
waves0.5 Hz < f < 10 HzKAWs or whistlers?10 Hz < f
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Scenario for Short-Wavelength Turbulence Shaikh & Zank,
MNRAS, 400,1881 (2009)
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Three-Dimensional Whistler Particle-in-cell (PIC)
SimulationsBuneman particle-in-cell 3D EMPIC code.Homogeneous
magnetized electron-ion plasma.Initial conditions:Turbulence:
Almost isotropic spectrum of whistler fluctuations at kc/pe <
1.Instability: Te/T||e > 1 leads to whistler anisotropy
instability.
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3D PIC Simulations of Whistler Turbulence Chang et al. (2011),
Geophys. Res. Lett., 38, L22102. Gary et al. (2012), Astrophys. J.,
755, 142 (Variations with initial wave amplitude). Chang et al.
(2013), J. Geophys. Res., 118, 2824 (Variations with e).Chang et
al. (2014), Phys. Plasmas, 21, 052305 (Linear vs. nonlinear
dissipation).Gary et al. (2014), J. Geophys. Res., 119, 1429
(Whistler anisotropy instability).Hughes et al. (2014), Geophys.
Res. Lett., 41, 8681 (Electron and ion heating).Chang et al.
(2015), Astrophys. J., in press (Inverse vs. forward cascade)
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3D PIC Simulations of Whistler Turbulence: Forward vs. Inverse
CascadesRun 2: Large-box simulationInitial spectrum:0.24 < kc/pe
< 0.49Fluctuation energy in forward cascade ~ 80 times greater
than energy in inverse cascade.So from here on, we emphasize
forward cascade results.
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3D PIC Simulations of Whistler Turbulence:Forward
CascadeMagnetic fluctuations show:Whistler-like dispersionDecay of
energy* Likely cause: wave-particle interactions (Electron Landau
damping)Forward cascade to larger wavenumbers and k >> k||*
Likely cause: Wave-wave interactionsSpectral break at kc/pe ~ 1*
Likely causes: Dispersion + dissipation
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3D Whistler Turbulence:Satisfies Linear Whistler
DispersionColors: Dispersion from PIC simulations.Black lines:
Dispersion from linear kinetic dispersion theory.
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2D Whistler Turbulence:Magnetic Fluctuation RatiosSaito et al.
[2008]Circles: 2D PIC simulation of whistler turbulence.Dashed
lines: Linear kinetic dispersion theoryRed: |B|||2/|B|2 Blue:
|B|2/|B|2 Green: |B|2/|B|2
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3D Whistler Turbulence:Dissipation Rate Increases with
Increasing e
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3D Whistler Turbulence:Wavevector Anisotropy Decreases with
e
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3D Whistler Turbulence: Spectral BreakPIC simulations at e=0.1
[Gary et al., 2012] have spectral break at kc/pe~1.But no universal
power-law scaling; rather, slopes become less steep as initial
amplitude is increased.
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Turbulent DissipationForward cascade of turbulence carries
fluctuating field energy to dissipation at short wavelengths.
Possible mechanisms:Linear wave-particle interactions:* Landau
damping.* Cyclotron damping.Nonlinear Landau damping.Nonlinear
reconnection at small-scale current sheets. Nonlinear nonresonant
stochastic heating.
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3D Whistler Turbulence:Electron HeatingElectron heating rate
increases with increasing e.Forward cascade yields k >> k||,
yielding E||, yielding electron heating with T||e > Te.
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3D Whistler Turbulence:Linear Damping vs. Total DissipationTotal
damping rates: solid lines.Linear theory damping rates: dashed
lines. Agreement at high e and low initial fluctuation amplitudes
(e).Chang et al. (2014)
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3D Whistler Turbulence:Scaling with Simulation Box SizeLpe/c =
25.6 (black lines)Lpe/c = 51.2 (blue lines)Lpe/c = 102.4 (red
lines)
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Whistler Anisotropy Instability: Particle-in-cell Simulation3D
PIC simulation in homogeneous plasma [Gary, Hughes et al.,
2014].Fluctuating fields driven by the instability grow, saturate,
then gradually decay.Wave-particle scattering reduces electron
anisotropy, but does not yield full isotropy.
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3D Whistler Turbulence:Satisfies Linear Whistler
DispersionTurbulence from initial whistler fluctuations:Dashed
line: Linear dispersion theory.Turbulence from whistler anisotropy
instability:Dashed line: Linear dispersion theory.
- Whistler Anisotropy Instability: Spectral EvolutionEarly times:
Short-wavelength whistler instability grows at kc/pe ~ 1 with k
> k||Forward cascade to very short wavelengths and k
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Whistler Anisotropy Instability:Anisotropy Upper
BoundInstability constrains value of Te/T||e. PIC simulation [Gary
& Wang, 1996]:Magnetosheath observations [Gary et al.,
2005]:
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3D PIC Simulations of Whistler Turbulence Cascades:
ConclusionsForward cascade 80 x faster than inverse cascade.
Forward cascade yields k >> k|| wavevector anisotropy.Two
distinct power-law spectra with break at kc/pe~1.At weak amplitudes
fluctuationsSatisfy linear theory dispersion.Heat electrons by
Landau damping with T||e > Te.Heat ions by Landau damping with
T||i < Ti.
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Conclusions: Whistler Turbulence Scaling RelationsIncreasing e
yieldsFaster forward cascade rates.Less anisotropic magnetic
spectra.Less anisotropic electron velocity distributions.Hotter
electron velocity distributions.Increasing simulation box size
yieldsWeaker overall dissipation.Stronger ion heating.Weaker
electron heating.