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TOWARD PREDICTING VLF TRIGGERING

MURI Workshop

3 March 2008

E. Mishin and A. Gibby Boston College ISR

Stanford University STAR Lab

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OUTLINE

Experimental constraints

Significance of plasmaspheric hiss: Step-like electron distribution

Results of ongoing study

OBJECTIVE: Specify VLF triggering conditions

APPROACH

Compare the occurrence of VLF triggering from the Siple transmitter with the magnetic activity and natural VLF emissions

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Perturbed plasmasphere contains density irregularities

Substorms/storms inject ~10-keV electrons into the plasmasphere

Energetic electrons remain trapped inside the PP for many hours

Necessary conditions for VLF triggering:

Background (unstable) population of >10-keV electrons

Field-aligned plasmaspheric density enhancements (ducts)

substorm aftermath

too vague condition to be useful for predictions

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Hiss Chorus: Natural triggering events (BroadBandE DiscreteE)

R: Rising chorus emission growing from the top of the hiss band

GEOTAIL [Nunn et al., 1997]R

F

85 dB/s

Nunn et al.’ simulation results

The distribution function observed in situ

yields only 10 dB/s Theory failure? DF and amplification must be considered in detail

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Step-like DF: Significance of plasmaspheric hissafter Trakhtengerts + [ 1985-2003]

The “temperature” anisotropy

Eq. pitch-angle

energy

The maximum frequency of hiss

moderately-strong hiss wave-particle interaction leads to diffusion over pitch-angles and precipitation of resonant

particles. In a steady-state, a sharp

increase (step) forms near the separatrix.

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Amplification of a ducted VLF wave

smooth = (2-6) • 0

Broad frequency range

dB

linear growth rate

dB

Step-like EDF

(ka)1/3 = 10-20

A wavelet on the top of the hiss band, f /fmax=1+ (ka)-2/3, gains most

Loss-cone“temperature” anisotropy

[dB] = 4.3•

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Triggering from the Siple VLF transmitter

Database:

June 1986 campaign (at dawn)

Auroral and RC indices

“Operator’s records”

APPROACH

Compare the occurrence of VLF triggering from Siple with (1) previous magnetic activity and (2) the current background VLF noise

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Triggering from Siple (cont’d)

Dst = -(30-40) nT

June 1986

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Triggering from Siple (cont’d)

+ fSiple * fav hiss

chorus pow.line

. whistler o nat. trigg. x sferics

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SUMMARY

•Most favorable conditions for VLF triggering in the morning sector seem to be satisfied after weak/moderate substorms.

•The triggering occurred when broad-band hiss emissions were present and the pump frequency was above the top of the hiss band.

•Consistent with theory, which is based on the second-order resonance and accounts for the step-like background electron distribution formed due to interaction with broad-band hiss.

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Formation of a step-like DF

is the Heaviside step function I ┴ = m· is the 1st adiabatic invariant

W = m·= is the kinetic energy

bounce period

diffusion time

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Schematic of VLF triggering

•Propagating toward the equator, ducted pump signals gain energy from background energetic electrons, being amplified by 20-40 dB.

•Near the magnetic equator, phase-trapping of resonant electrons by the amplified pump wave results in the formation of a phase-coherent, quasi-monoenergetic electron beam.

•The beam generates narrow-band VLF emissions with falling or rising frequency. Their sweep rates (~1 kHz/s) satisfy the (generalized) second-order resonance (beam-wave phase coherence ).

SIPLE

receiver

notably, Helliwell +STAR team, Sudan , Nunn, Karpman+ , Omura, Matsumoto, Trakhtengerts+

L=4.2