1. Nonlinear VLF Wave Physics in the Radiation Belts Chris Crabtree Guru Ganguli Erik Tejero Naval Research Laboratory Leonid Rudakov Icarus Research Inc. PSG1: 1) Does the presence of NL waves affect the conclusion that QL acceleration suffices? PSG2: 6) How important are NL wave interactions in precipitation loss? NL Wave Interactions: 1.Introduce a new time scale and new physics. 2.Lead to an wave energy dependent distribution of waves. 3.Can lead to enhanced precipitation under right conditions. 4.Has implications for standard assumptions in analyzing wave data.

2. Van Allen Probe A in morning sector at L~5.5 in Equatorial Plane on Oct 14, 2012 Whistler Mode Chorus

3. Burst Mode Data Standard Single Wave Analysis

4. Chorus Sub-packet Structure: Initial Evidence for NL Wave Physics

5. Triggered Emissions Triggered emissions observed in laboratory experiments. Launched Whistler Triggered Emission

6. Whistler Chorus-like Emissions Chorus-like emissions observed in laboratory experiments. Whistler Chorus-like Emission Beam Generated Mode

7. (n=0 Toroidal Mode Number) MHD Chirping in JET

8. Beyond Quasi-linear Theory: The Basic NL Building Blocks Induced scattering by radiating low frequency wave – Waves energy and momentum are conserved Induced scattering by plasma particles – Wave momentum need not be conserved if particles are magnetized (principal momentum conserved) Resonance Condition Decay Coalescence – Frequency decreases slightly while wave scatters Induced Scattering (nonlinear Landau damping)

9. Diffusion, Quasi-Linear, Nonlinear: Terminology Diffusion

10. NL scattering transfers energy from Electrostatic to Electromagnetic Waves Lower Hybrid Magnetosonic Whistler small group velocity Lower Hybrid with large group velocity Whistler Magnetosonic large group velocity NL Scattering can drastically change the wave-vector while decreasing the frequency a small amount.

11. Effects of Scattering on Ray Trajectory Formation of Whistler Wave Cavity [Crabtree et al. 2012]. Multi-pass Whistler Amplification [Ganguli et al. 2012].

12. NL Scattering can Allow for Multi-Pass Convective Gain V || Loss Cone Trapped Population  Loss Cone Distribution leads to convective amplification of whistlers [Kennel & Petschek 1966] Flux of energetic electrons required for substantial growth is too large, Because the effective interaction time is too small. NL Scattering can effectively increase the interaction time and allow for multi-pass gain [Ganguli et al., 2012] Flux for typical storm is used (4x10 5 /cm 2 /s/sr), large storms can have much larger fluxes Distribution A: Unlimited distribution

13. Laboratory Demonstration of Nonlinear Generation of Whistler Waves Frequency Spectrum Wave Vector Spectrum EMES Nonlinear Conversion of ES Lower Hybrid Waves into EM Whistler Waves θ~85˚ B plasma NRL Space Chamber Electrostatic waves are launched from an antenna When the launched wave amplitude is large enough nonlinear scattering is triggered A spectrum of electromagnetic waves is observed Launched Observed

14. Validation of Wave Distribution Function Methodology plasma density =3 x 10 10 cm -3 (argon) B = 50 G ω pe /ω ce = 11 pump = 10.0 MHz ~ 20 ω LH WDF 2D Scan 10 Mhz 9.96 Mhz

15. Three Wave Decay was also observed High Frequency Low Frequency FrequencySVDWDF 10 MHzθ=55˚±2˚θ=85˚±1˚ 9.805 MHzθ=80˚±8˚θ=86˚±1˚ 195 kHzθ=6˚±4˚θ=0˚±2˚

16. Plasmaspheric Hiss Van Allen Probe A located at L~4.6 and MLT~4.9

17. Lightening generated whistlers propagating through Hiss Hydrogen Lower-hybrid frequency~1 kHz Falling tone lasts 1.5 s FFT Window ~ 15 wave periods

18. 717 Hz, 2.297 s 649 Hz, 2.428 s

19. Van Allen Probe Evidence of NL Scattering 649 Hz, 2.428 s (pump wave) 581 Hz, 2.428 s (scattered wave) Large azimuthal angle change.

20. Nonlinear Scattering 547 Hz 512 Hz

21. Comparison of Wave Distribution Function ω pe /ω ce = 11 pump = 10.0 MHz ~ 20 ω LH WDF 10 Mhz 9.96 Mhz

22. Consideration of NL Wave Interactions Introduces a new time scale and new physics. Allows redistribution of wave energy in frequency and wave- vector space. Leads to a wave energy dependent distribution of waves. May play role in explaining variability of electron lifetime. Can lead to enhanced precipitation under right conditions. Formation of whistler wave cavity Has implications for standard assumptions in analyzing wave data. The assumption of a single wave-vector is likely invalid.

23. NL Scattering allows for New Dynamics Electrostatic Solutions of WKE: Electromagnetic Solutions of WKE: Solution of the Wave kinetic equation, in periodic box, which conserves plasmon number, and in simple cases has analytical shock-like solution. Shock Like Distribution A: Unlimited distribution

24. Including NL scattering in QL simulation of VRI generates Electromagnetic Waves Solving the Wave-Kinetic Equation: 3D Electromagnetic PIC simulation: Linear Nonlinear [Winske & Daughton 2012] NL terms add Additional Time Scale and Slow down diffusion

25. Whistler Wave Cavity Can Form