Nonlinear VLF Wave Physics in the Radiation Belts

Chris Crabtree Guru Ganguli Erik TejeroNaval Research Laboratory

Leonid RudakovIcarus 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.

Van Allen Probe A in morning sector at L~5.5 in Equatorial Plane on Oct 14, 2012

Whistler Mode Chorus

Burst Mode Data

Standard Single Wave Analysis

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

Triggered Emissions

Triggered emissions observed in laboratory experiments.

LaunchedWhistler

Triggered Emission

Whistler Chorus-like Emissions

Chorus-like emissions observed in laboratory experiments.

Whistler Chorus-like Emission

Beam Generated Mode

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

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)

0)()/()/(

kkee NkrmnvvnAcneP

),,/(

,

31

321321

is lckMSLH

kkk

||2||1

21||v kke

Resonance Condition

11,k

22 ,k

1v

2v

Decay Coalescence

33 ,k

22 ,k

11,k

33 ,k

22 ,k

11,k

ste ckkkk ||,v||min~ 21||2||1

– Frequency decreases slightly while wave scatters

Induced Scattering(nonlinear Landau damping)

Diffusion, Quasi-Linear, Nonlinear: Terminology

Diffusion

NL scattering transfers energy from Electrostatic to Electromagnetic Waves

Lower Hybrid

Magnetosonic

Whistler

small groupvelocity

Lower Hybrid

withlarge group velocity

WhistlerMagnetosonic

large group velocity

NL Scattering can drastically change the wave-vector while decreasing the frequency a small amount.

Effects of Scattering on Ray Trajectory

Formation of Whistler Wave Cavity [Crabtree et al. 2012].Multi-pass Whistler Amplification [Ganguli et al. 2012].

NL Scattering can Allow for Multi-Pass Convective Gain

V||

Loss Cone

TrappedPopulation

• 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 (4x105 /cm2/s/sr), large storms can have much larger fluxes

Distribution A: Unlimited distribution

Laboratory Demonstration of Nonlinear Generation of Whistler Waves

Frequency Spectrum Wave Vector Spectrum

EM ES

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

Validation of Wave Distribution Function Methodology

plasma density =3 x 1010 cm-3 (argon)B = 50 G

ωpe/ωce = 11pump = 10.0 MHz ~ 20 ωLH

WDF

2D Scan 10 Mhz

9.96 Mhz

Three Wave Decay was also observedHigh FrequencyLow Frequency

Frequency SVD WDF

10 MHz θ=55˚±2˚ θ=85˚±1˚

9.805 MHz θ=80˚±8˚ θ=86˚±1˚

195 kHz θ=6˚±4˚ θ=0˚±2˚

Plasmaspheric Hiss

Van Allen Probe A located at L~4.6 and MLT~4.9

Lightening generated whistlers propagating through Hiss

Hydrogen Lower-hybrid frequency~1 kHz

Falling tone lasts 1.5 s

FFT Window ~ 15 wave periods

717 Hz, 2.297 s

649 Hz, 2.428 s

Van Allen Probe Evidence of NL Scattering649 Hz, 2.428 s (pump wave)

581 Hz, 2.428 s (scattered wave)

Large azimuthal angle change.

Nonlinear Scattering547 Hz

512 Hz

Comparison of Wave Distribution Function

ωpe/ωce = 11pump = 10.0 MHz ~ 20 ωLH

WDF

10 Mhz

9.96 Mhz

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.

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

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

Whistler Wave Cavity Can Form