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 The simulation domain ( X-Y ) is 51.2 and 25.6 electron inertial lengths. Two Cases: where θ is the angle between B o and X direction.

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 0<Ω ce t<200 0<Ω ce t<650 mother whistler wave mother/daughter whistler waves whistler waves LH/MS waves 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. Wavenumber Power Spectrum (Ω ce t=150) whistler waves

12. (Ω ce t=300) Wave Number Power Spectrum whistler mother whistler daughter LH/MS daughter whistler waves Decay of the whistler waves is evident with inclined B 0.

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

14. Ion Distribution Function and Energy History Ω ce t=450 Ion heating is relatively small However, at 60 o the heating appears to be preferentially perpendicular to B 0

15. Electron Distribution Function and Energy History Ω ce t=450 Electron tail heating is preferentially parallel to B 0 and increased at 60 0. 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 predicted by weak turbulence theory. The simulation results indicate that 3D physics of whistler evolution is important for nonlinear wave scattering. Such behavior is not observed in recent simulation work which does not consider 3D effects. Further investigations are being undertaken to access the impact of such wave scattering processes on whister turbulence.