nonlinear vlf wave physics in the radiation belts chris crabtree guru ganguli erik tejero naval...
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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.
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Van Allen Probe A in morning sector at L~5.5 in Equatorial Plane on Oct 14, 2012
Whistler Mode Chorus
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Burst Mode Data
Standard Single Wave Analysis
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Chorus Sub-packet Structure: Initial Evidence for NL Wave Physics
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Triggered Emissions
Triggered emissions observed in laboratory experiments.
LaunchedWhistler
Triggered Emission
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Whistler Chorus-like Emissions
Chorus-like emissions observed in laboratory experiments.
Whistler Chorus-like Emission
Beam Generated Mode
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(n=0 Toroidal Mode Number) MHD Chirping in JET
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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)
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Diffusion, Quasi-Linear, Nonlinear: Terminology
Diffusion
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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.
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Effects of Scattering on Ray Trajectory
Formation of Whistler Wave Cavity [Crabtree et al. 2012].Multi-pass Whistler Amplification [Ganguli et al. 2012].
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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
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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
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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
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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˚
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Plasmaspheric Hiss
Van Allen Probe A located at L~4.6 and MLT~4.9
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Lightening generated whistlers propagating through Hiss
Hydrogen Lower-hybrid frequency~1 kHz
Falling tone lasts 1.5 s
FFT Window ~ 15 wave periods
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717 Hz, 2.297 s
649 Hz, 2.428 s
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Van Allen Probe Evidence of NL Scattering649 Hz, 2.428 s (pump wave)
581 Hz, 2.428 s (scattered wave)
Large azimuthal angle change.
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Nonlinear Scattering547 Hz
512 Hz
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Comparison of Wave Distribution Function
ωpe/ωce = 11pump = 10.0 MHz ~ 20 ωLH
WDF
10 Mhz
9.96 Mhz
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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.
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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
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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
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Whistler Wave Cavity Can Form