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|

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

Scenario for Short-Wavelength Turbulence Shaikh & Zank, MNRAS, 400,1881 (2009)

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.

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)

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.

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

3D Whistler Turbulence:Satisfies Linear Whistler DispersionColors: Dispersion from PIC simulations.Black lines: Dispersion from linear kinetic dispersion theory.

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

3D Whistler Turbulence:Dissipation Rate Increases with Increasing e

3D Whistler Turbulence:Wavevector Anisotropy Decreases with e

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.

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.

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.

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)

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)

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.

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

Whistler Anisotropy Instability:Anisotropy Upper BoundInstability constrains value of Te/T||e. PIC simulation [Gary & Wang, 1996]:Magnetosheath observations [Gary et al., 2005]:

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.

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.