Nonlinear Evolution of Whistler Turbulence

1. Nonlinear Evolution of Whistler Turbulence W.A. Scales, J.J. Wang, and O. Chang Center of Space Science and Engineering Research Virginia Tech L. Rudakov, G. Ganguli, and M. Mithaiwala Plasma Physics Division Naval Research Laboratory

2. Outline • Introduction and Motivation • Simulation Model • Simulation Results • Summary, Conclusions and Future Work

3. Motivation • Recent 2D simulation work has considered the evolution of whistler turbulence which indicates a cascade from long to short spatial scales (e.g Saito et al, 2008). • Such simulations may be limited and not allow development of important nonlinear wave-wave processes that may ultimately impact wave-particle interaction processes for whistler waves.

4. Objective • Perform 2.5D fully electromagnetic PIC simulations to study the evolution of whistler turbulence • Access the role of nonlinear wave-wave processes • Compare to predictions of previous simulation works on the turbulence cascade process • Begin to access the impact on the generation of whistler turbulence

5. Important physics not resolved in past simulation work • Past simulation work considered in the simulation plane • For at an inclination to the simulation plane, it is predicted that whistler waves decay and coalescence to produce an inverse cascade (short to long wavelengths) • The important new physics is represented through the term

6. Importance of 3D physics • In the case Te = Ti the high frequency whistlers can radiate lower hybrid/magneto-sonic (LH/MS) waves. • The decay rate, assuming a narrow frequency band is given by • In 2D (the Saito et al. case), this rate is zero because

7. Simulation Setup • To consider an inverse cascade from high to low frequency, and initial perturbation is used to seed whistler turbulence • The perturbation is taken to be heavy negative particles (“muon”) with a velocity ring in phase space. • Once the whistler waves are generated, their nonlinear evolution is studied.

8. Simulation Domain • Thesimulationdomain ( X-Y ) is 51.2 and 25.6 electroninertiallengths. • Two Cases: whereθistheanglebetweenBo and Xdirection.

9. Magnetic Field Energy • Whistler waves linearly grow from the free energy in the perturbation • in both configurations • The nonlinear evolution is quite different

10. Frequency Power Spectrum mother whistler wave 0<Ωcet<200 whistler waves mother/daughter whistler waves LH/MS waves whistler waves 0<Ωcet<650 • For the case with inclination, whistler waves decay into lower hybrid/magnetosonic • waves as predicted by weak turbulence theory. • Without inclination, this decay is not apparent.

11. WavenumberPower Spectrum (Ωcet=150) whistler waves whistler waves

12. Wave Number Power Spectrum (Ωcet=300) LH/MS daughter whistler mother whistler waves whistler daughter • Decay of the whistler waves is evident with inclined B0.

13. Wave Number Power Spectrum (Ωcet=450) whistler waves LH/MS daughter • At later times, the LH/MS waves become more prominent in the spectrum.

14. Ion Distribution Function and Energy History Ωcet=450 • Ion heating is relatively small • However, at 60o the heating • appears to be preferentially • perpendicular to B0

15. Electron Distribution Function and Energy History Ωcet=450 • Electron tail heating is preferentially • parallel to B0 and increased at 600. • Electron heating is more significant • that ion heating

16. Summary • Nonlinear scattering of whistler waves by radiating low frequency LH/MS waves is observed in numerical simulations, as predictedbyweakturbulencetheory. • The simulation results indicate that 3D physics of whistler evolution is important for nonlinear wave scattering. • Suchbehaviorisnotobserved in recentsimulationworkwhichdoesnotconsider 3D effects. • Furtherinvestigations are beingundertakentoaccesstheimpact of such wave scatteringprocessesonwhisterturbulence.