The Role of VLF Transmitters in Limiting the Earthward Penetration of Ultra-Relativistic Electrons in the Radiation Belts J. C. Foster, D. N. Baker, P.J. Erickson, J. M. Albert, J. F. Fennel, E. V. Mishin, M. J. Starks, A. Jaynes, X. Li, S. G. Kanekal 1

Observations Earth is surrounded by a magnetically-confined VLF bubble Propagation characteristics cause VLF Tx wave intensity to build up at their reflection point where Tx frequency ≅ ½ f ce. For the strongest Tx at ~20 kHz, this occurs near L=2.8 Outer zone highly-relativistic electrons encounter a “barrier” to inward penetration near L=2.8 [Baker]. Stormtime recovery of outer zone involves local acceleration by chorus waves outside the plasmapause [Reeves, Thorne] During the 17 March 2015 storm, with the plasmapause eroded to L~2, steep gradients formed at L~2.8. 2

Meridional section of power flux predicted by AFRL’s VLF Propagation Code in the plasmasphere due to NPM transmissions. The transmitter is marked by a triangle. Note the prominent shadow boundary in the conjugate hemisphere. An analogous boundary (not visible) exists in the transmitter hemisphere. [Starks et al, 2009] Propagation of VLF Waves in Inner Magnetosphere The VLF Bubble Frequency (kHz) Dipole L 3

½ fce NAA 10 5 Increase 4

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These observations are strongly suggestive of a previously unrecognized fast acting (≤ 1 day) and spatially localized (≤ 0.5 R E ) mechanism responsible for the formation of such a well-defined gradient outside the plasmapause during the active recovery of outer zone relativistic electrons. 7

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Stimulated emissions and Mode Conversion at the Outer Edge of the VLF Bubble At 18:30 UT, with the plasmapause near L ~ 2.6, strong enhancement of electric field intensity around the 21.4 kHz NPM Tx frequency extended beyond the ½ f ce limit to L ~ 3.2 Unstable distributions of 100s keV injected electrons and heating of super- thermal (10s eV) O+ ions by parametric instabilities were observed at the edge of the VLF bubble. Near the cusping/reflection region at the plasmapause, the VLF Tx wave becomes nearly electrostatic and mode conversion (coelescence) to wave modes near the LH frequency (~700 Hz) occurs ~700 Hz low frequency modes (particularly ion Bernstein)) are observed spatially coincident with the region of amplification at the transmitter frequency Resonant interactions between multi-MeV electrons and ≤ 700 Hz waves at small pitch angles accelerate particle loss to the atmosphere through scattering into the drift loss cone. 9

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Multi-Step Electron Resonances Fully-relativistic resonant electron energies (n=-1) are calculated for the observed profiles of N e and B In the low density region outside the plasmapause: Abundant 100s keV electrons amplify VLF waves near Tx frequency kHz waves parametrically couple to 700 Hz f LRH wave modes Butterfly pitch angle distributions for MeV electrons inside L ~ 3.5 are in resonance with 21.4 kHz VLF waves at ~70 deg pitch angle. MeV electrons at small pitch angle are in resonance with 700 Hz waves and are scattered into the drift loss cone. 12

MeV Electrons at Large Pitch Angle Resonance with Butterfly Distribution MeV Electrons at Small Pitch Angle Scattering into Loss Cone keV Electrons at Small Pitch Angle Stimulated Emissions at Tx Frequency 13

Localized Electron Precipitation Parametric coupling of waves modes and electron resonances at the outer edge of the VLF bubble create a localized loss mechanism near L ~ 2.8 that limits the inward extent of local acceleration of MeV electrons during storm recovery Migration of MeV electrons into drift loss cone is observed inside L ~ 3.2 coincident with range of stimulated Tx emissions South Atlantic magnetic anomaly defines the drift loss cone SAMPEX observes continuous MeV precipitation flux outside SAA Evidence for continuous precipitation mechanism near L=2.8 14

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Diffusion Inside the Barrier Strong local acceleration outside L ~ 3 during 17 March 2015 storm resulted in continual inward diffusion of multi-MeV electrons inward of L = 2.8 once the plasmapause expanded beyond L ~ 3. Losses and recovery of outer zone electrons during the subsequent 22 June 2015 storm resulted in the formation of a “remnant 3 rd belt” inside L ~

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Effects of Inward Diffusion and Adiabatic Acceleration Observed in REPT-A 3.4 MeV Channel 20 L=2.8

Happy Halloween 21

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Mode conversion The dispersion relation of an oblique whistler wave in cold plasma is expressed as k 2 c 2 ω 2 =1-ω pe 2 /(ω(ω-ω ce cosϑ)), where ω pe /ω ce is the electron plasma/cyclotron frequency and cosϑ=k || /k. When ω approaches ω ce cosϑ, the wave becomes quasi electrostatic (kc/ω→∞) and has a resonance cone character. The dispersion relation of low-frequency, ω >m e /m i. Here m e /m i is the electron/ion mass and ω lhr =m e /m i ω ce at ω pe /ω ce >>1 is the lower hybrid resonance frequency. Near the resonance cone, a whistler wave is effectively transformed by this pathway into a slowly-moving oblique electrostatic wave with the greatly-increased amplitude. 23