1. 1 TOWARD PREDICTING VLF TRIGGERING MURI Workshop 3 March 2008 E. Mishin and A. Gibby Boston College ISR Stanford University STAR Lab

2. 2 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

3. 3  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

4. 4 Hiss  Chorus : Natural triggering events (B road B and E  D iscrete E) 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

5. 5 Step-like DF: Significance of plasmaspheric hiss after 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.

6. 6 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 /f max =1+ (ka) -2/3, gains most Loss-cone  “temperature” anisotropy  [dB] = 4.3 

7. 7 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

8. 8 Triggering from Siple (cont’d) Dst = -(30-40) nT June 1986

9. 9 Triggering from Siple (cont’d) + f Siple * f av hiss  chorus  pow.line. whistler o nat. trigg. x sferics

10. 10 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.

11. 11 Formation of a step-like DF  is the Heaviside step function I ┴ = m·  is the 1 st adiabatic invariant W = m·  =  is the kinetic energy bounce period diffusion time

12. 12 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