1. Pitch-Angle Scattering of Relativistic Electrons at Earth’s Inner Radiation Belt with EMIC Waves Xi Shao and K. Papadopoulos Department of Astronomy University of Maryland College Park, MD 20742

2. Motivation Gyro-resonant Pitch Angle Scattering with Low Frequency (ω < Ω i ) Wave Have discussed Scattering of Relativistic Protons with Alfven wave Have discussed efficient ways to generate ULF waves. Scattering of Relativistic Electrons with Electromagnetic Ion- Cyclotron (EMIC) Wave Dispersion Relation for Parallel Propagation

3. Minimum Energy (Emin) vs. k for Gyro- Resonant Interaction with Electron k > k0 for E min < 1MeV k0 Gyro-Resonant Condition of Relativistic Electron For conditions at equator, L = 2 To resonant-scatter 1 MeV electrons, wave-vector needs to satisfy k > k0.

4. O+ gyro-frequency along L = 2 field line Density of Electron, H+, He+, O+ along L = 2 dipole magnetic field line (from GCPM) Along L=2 magnetic field line Equator Earth Equator

5. Dispersion Relation for L Mode with Multi-Ion (H+, He+,O+) Species Parallel Wave Number ω=kV A Dispersion Relation of EMIC Waves

6. Dispersion Relations for L- Mode EMIC Wave For conditions at equator, L =2; f H+ = 60 Hz. E min of Gyro-resonant Electron with He+ Band Magnetic field: dipole Plasma Density: GCPM Gyro-resonant Scatterings of Electron by EMIC Wave (along L=2 magnetic field line) 1 MeV

7. Ray-Tracing of Multi-Frequency (within He+ band) EMIC Wave (along L=2 field line) Piling-up Factor (1/(Vg*A)) Group Velocity Vg along Ray Path Ray Tracing Applicable

8. Interaction Region of Gyro-resonant Scattering of Electrons by Broad-Band Wave within He+ Band f 0 = 15.72 Hz Δf = 0.05 f 0 14.94 Hz 16.5 Hz Interaction Region with 1 MeV Electron Latitude Range: 7.85 degree. Distance Range along Field Line: ~1800 km. Pitch Angle Range: 0 – 88 degree. 1 MeV

9. Pitch Angle Diffusion Analysis Quasi-linear diffusion analysis –Small scattering with each wave –Gaussian-shape spectrum –Diffusion is proportional to wave power Local Diffusion Rate: Bounce Averaged Pitch Angle Diffusion Equation: Bounce Averaged Diffusion Rate: (Life Time) Summers and Thorne, 2003 Lyons and Williams, 1984

10. f 0 = 14.94 Hz Δf = 0.05 f 0 Pitch-Angle Diffusion Rate for Electrons (along L = 2) Co-Latitude =85.48 deg. δB = 300 pT f 0 = 15.72 Hz Δf = 0.05 f 0 400 W input, ΔL=0.1 Local Diffusion Rate Bounce-Averaged Diffusion Rate 1MeV Electron

11. Life Time and Equilibrium Equatorial Particle Flux Distribution Equilibrium Distribution Function g(α 0 ) vs. Pitch Angle α 0 400 W power input over shells ΔL=0.1, L=2 Life time= 5.2 days f 0 = 15.72 Hz Δf = 0.05 f 0 He+ Branch EMIC Wave 1MeV Electron

12. Conclusions Scattering of relativistic particles into loss- cone through low-frequency waves ( ω < Ω i ) provide viable ways to do inner (Proton and Electron) radiation belts remediation. For electron belt remediation, need to have better understanding of the resonant- absorption, reflection, tunneling, mode- conversion of EMIC waves at resonant region. Need to include full-wave effects.

13. Electron (> 300 keV) Belt Dynamics (1979-1999) (from NOAA 5-14 POES Satellites) Inner (peak near L=1.6 ) and Outer (peak near L= 4-5) Electron Belts; Slot Region (L=3). Variability of outer belt; Relative stable inner belt. Hazardous to satellites, astronauts, and spacecraft. 21 years