Laboratory Investigation of Nonlinear Whistler Wave Processes*

Erik Tejero, Chris Crabtree, Lon Enloe, David

Blackwell, Bill Amatucci, Guru Ganguli

erik.tejero@nrl.navy.milPlasma Physics Division, Naval Research Laboratory

*Work supported by NRL base program and NASA Grant No. NNH17AE70I

March 8, 2018 2

NRL Space Physics Simulation Chamber

Chapman Conference on Particle Dynamics in the Earth’s Radiation Belts – Cascais, Portugal

Collaborators

March 8, 2018 3

• Laboratory Experiments

‒ Lon Enloe (NRL)

‒ Bill Amatucci (NRL)

• Theory

‒ Chris Crabtree (NRL)

‒ Guru Ganguli (NRL)

• Space Observations

‒ David Malaspina (UC Boulder)

• Simulations

‒ Dong Lin (VA Tech)

‒ Wayne Scales (VA Tech)

Chapman Conference on Particle Dynamics in the Earth’s Radiation Belts – Cascais, Portugal

Studying the Building Blocks of Weak Turbulence

March 8, 2018Chapman Conference on Particle Dynamics in the

Earth’s Radiation Belts – Cascais, Portugal4

pump

scatteredwaves

Nonlinear Scattering

Tejero et al., Phys. Plasmas, 22, 091503 (2015)

Parametric Decay

pump

daughterwaves

Verification of Nonlinear Conversion of ES to EM

March 8, 2018Chapman Conference on Particle Dynamics in the

Earth’s Radiation Belts – Cascais, Portugal5

B/B0 ~ 510-6 , NL= L

𝑘⊥ Τ𝑐 𝜔𝑝𝑒 > 1

10 MHz 9.96 MHz

Δ𝜔

Δ𝑘∥𝑣𝑡𝑒~1

2

Tejero et al., Sci. Rep., 5, 17852 (2015) and Tejero et al., Phys. Plasmas, 23, 055707 (2016)

gNL

k1®k 2 ~w

pe

2

wk 2

k2

2

1+ k2

2

Wk1

n0T

(k1´ k

2)

||

2

k^1

2 k^2

2k1

å zeIm Z

wk 2

-wk1

k||2

- k||1

vte

æ

è

çç

ö

ø

÷÷

Amplitude Scaling90° turning

Resonance Condition

𝛾𝐿 𝑘,𝜔 = 𝛾𝑁𝐿 𝑘,𝜔,𝑊

Threshold 10 MHz – Pump Wave

9.96 MHz – Scattered Wave

Experiment agrees with theory in detail

Wave Distribution Function Technique Validated

March 8, 2018Chapman Conference on Particle Dynamics in the

Earth’s Radiation Belts – Cascais, Portugal6

10 MHz – Pump Wave

9.96 MHz – Scattered Wave

Tejero et al., Phys. Plasmas, 22, 091503 (2015)

Results from WDF and spectral techniques are consistent with laboratory k measurements.

Histogram Results Using Spectral Techniques (SVD)

Triggered Emissions Experimental Setup

March 8, 2018 7Chapman Conference on Particle Dynamics in the Earth’s

Radiation Belts – Cascais, Portugal

Bz

20 G

mirror point

helical antenna hollow cathode

420 G

SPSC Source Chamber

SPSC Main Chamber

Plasma

Source

Triggered Emission Observed in Laboratory

March 8, 2018Chapman Conference on Particle Dynamics in the

Earth’s Radiation Belts – Cascais, Portugal8

𝐸𝑏 = 1.8 𝑘𝑒𝑉 𝐼𝑏 = 20 𝑚𝐴 → Τ𝑛𝑏 𝑛0 = 0.5 − 13% 𝛼 = 40°

Τ𝜔𝑝𝑒 Ω𝑒 = 1.75 − 9.2 Τ𝜔0 Ω𝑒 = 0.425

Nonlinear Scattering in Triggered Emission Data

March 8, 2018Chapman Conference on Particle Dynamics in the

Earth’s Radiation Belts – Cascais, Portugal9

23.8 MHz

𝛾 = 860 𝑠−1

Three Wave Decay in Triggered Emission Data

March 8, 2018Chapman Conference on Particle Dynamics in the

Earth’s Radiation Belts – Cascais, Portugal10

Chorus-like Emissions Exhibit Subpacket Structure

March 8, 2018Chapman Conference on Particle Dynamics in the

Earth’s Radiation Belts – Cascais, Portugal11

Chorus-like emissions observed in laboratory experiments.

Beam Generated Mode

March 8, 2018 12Chapman Conference on Particle Dynamics in the Earth’s

Radiation Belts – Cascais, Portugal

Laboratory Simulation of

Broadband Noise in Boundary Layers

Dubois

et

al., JG

R, 119,

5624 (

2014)

Broadband Electrostatic Noise

NRL Space Chamber

Scaled PSBL/Lobe Boundary

• Plasma Sheet/Lobe Boundary Layer

simulated by interpenetrating plasmas

• EIH wave generation around the lower

hybrid frequency relaxes boundary layer

• Results in lower frequency shear-driven

waves to form broadband electrostatic noise

KH𝝆𝒊 ≪ 𝑳𝑬𝝎 ≪ 𝜴𝒊

IEDDI𝝆𝒊 ~ 𝑳𝑬𝝎~𝜴𝒊

EIH𝝆𝒊 > 𝑳𝑬

𝜴𝒊 < 𝝎 < 𝜴𝒆

In Situ Observations of Dipolarization Fronts

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[Fu et al. 2012]

~𝛿𝑖 , ~𝜌𝑖

LH waves

Whistler waves

Self-consistent E-field Generation Observed in Lab

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Earth’s Radiation Belts – Cascais, Portugal14

• B = 65 G

• i = 2.2 cm

• e = 0.09 cm

[Divin et al. 2015]

i

Laboratory Experiments Verified EIH Instability

March 8, 2018 15Chapman Conference on Particle Dynamics in the Earth’s

Radiation Belts – Cascais, Portugal

Comparison of experimental data with theoretical

predictions for the Electron-Ion Hybrid Instability

Sheared transverse flows drive lower hybrid waves

EIH Instability Experimental Verification

March 8, 2018 16Chapman Conference on Particle Dynamics in the Earth’s

Radiation Belts – Cascais, Portugal Amatucci et al, Phys. Plasmas. (2003)

Amatucci et al, Phys. Plasmas. (2003)

i

lower hybrid eigenmode localized to the shear layer as in DF

Divin et al. Identified Lower Hybrid Drift Instability as Source of Observed Lower Hybrid Waves

March 8, 2018Chapman Conference on Particle Dynamics in the

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• 𝑘 ො𝑥𝜌𝑒 , 𝑘 ො𝑦𝜌𝑒 ~ −0.6, 0.3

• LHDI modes should be damped

[Divin et al. 2015]

Eigenmode has no single kx to Doppler shift

Reanalysis Shows that Sheared Flows Can Drive Observed Lower Hybrid Waves

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Density 𝑛 = 3.8 × 105 m−3

Magnetic Field 𝐵𝑧 = 26 nT

Ion Diamagnetic Drift 𝑉𝐷𝑖 = 1.9 × 105 m/s

Electric Field 𝐸𝑥 = −20 mV/m

EB Drift 𝑣𝐸 = 1.7 × 106 m/s

Electric Field GradientScale Length

𝐿𝐸 = 54 km

Wave Vector in EB Direction

𝑘𝑦 = 3 × 10−5 m−1

Relevant ParametersAnalysis Results

• LHDI: 𝑘𝑦𝜌𝑒~1

• EIH: 𝑘𝑦𝐿𝐸~1

𝑘𝑦𝜌𝑒 = 0.2 vs 𝑘𝑦𝐿𝐸 = 1.1

∆= −9.3

Conditions above threshold for EIH and wavelength is consistent.

• Propagates in EB direction

Whistler Waves Can Also Be Driven by Sheared Flows

March 8, 2018 19Chapman Conference on Particle Dynamics in the Earth’s

Radiation Belts – Cascais, Portugal

Whistler Waves Are Bursty, Chirping Waves

March 8, 2018 20

burs

t fr

equency

1/s

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Whistler Waves Exhibit Characteristics Consistent with Particle Trapping

March 8, 2018 21Chapman Conference on Particle Dynamics in the Earth’s

Radiation Belts – Cascais, Portugal

• f < 0.5 fce

• m = 1

• kz ~ 10 m-1

• Eres ~ 1-10 keV

Velocity Shear-driven Whistler Waves in Lab Are Observed with an Upper and Lower Band

March 8, 2018Chapman Conference on Particle Dynamics in the

Earth’s Radiation Belts – Cascais, Portugal22

• Large amplitude bursts

• Chirp both up and down

• Lower band has faster chirp rates

Summary

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• Dipolarization fronts provide a variety of sources of free energy to drive waves

• Laboratory experiments verified EIH instability theory

• Lab and theory results provide quantitative tests to determine source of waves

• Analysis demonstrates that sheared flows are capable of driving the observed lower hybrid waves

• Lab experiments demonstrate that electromagnetic whistler waves can also be driven by sheared flows

• Could observed whistler waves also be due to the EIH instability?

Chapman Conference on Particle Dynamics in the Earth’s Radiation Belts – Cascais, Portugal

Begun a coordinated study between lab, theory, modeling, and

space observations to study these waves at dipolarization fronts

Local Approximation Predicts Instability Threshold

March 8, 2018 24

ഥ𝜔3 + 2𝛿2

1 + 𝛿2

ത𝑉0ത𝑘𝑦

− ത𝑘𝑦 ത𝑉0 ഥ𝜔2 − ഥ𝜔 + ത𝑘𝑦 ത𝑉0 = 0

𝑎𝑥3 + 𝑏𝑥2 + 𝑐𝑥 + 𝑑 = 0

∆= 18𝑎𝑏𝑐𝑑 − 4𝑏3𝑑 + 𝑏2𝑐2 − 4𝑎𝑐3 − 27𝑎2𝑑2

If ∆< 0, then 1 real solution and two complex conjugate solutions

Effects of Nonuniform B on EIH• Increased growth rate• No effect on wavelength

Diamagnetic Drift Frequency: 𝜔𝐷𝑒,𝑖 = 𝑘𝑣𝐷𝑒,𝑖

Shear Frequency: 𝜔𝑠 =𝑑𝑣𝐸

𝑑𝑥

ഥ𝜔 =𝜔

𝜔𝐿𝐻, 𝛿 =

𝜔𝑝𝑒

Ω𝑒, ത𝑉0 =

𝑣𝐸

𝜔𝐿𝐻𝐿𝐸, ത𝑘𝑦 = 𝑘𝑦𝐿𝐸

predicted threshold

Chapman Conference on Particle Dynamics in the Earth’s Radiation Belts – Cascais, Portugal