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Transport in the Radiation Belts and the role of Magnetospheric ULF Waves

Transport in the Radiation Belts and the role of Magnetospheric ULF Waves. Scot R. Elkington LASP, University of Colorado. GEM 2003 Snowmass, CO. With many thanks to:

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Transport in the Radiation Belts and the role of Magnetospheric ULF Waves

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  1. Transport in the Radiation Belts and the role ofMagnetospheric ULF Waves Scot R. Elkington LASP, University of Colorado GEM 2003 Snowmass, CO With many thanks to: D. N. Baker, D. H. Brautigam, A. A. Chan, Y. Fei, J. Green, M. K. Hudson, X. Li, K. L. Perry, E. J. Rigler, and M. J. Wiltberger S. Elkington, GEM 2003

  2. Outline • Introduction to radiation belts. • Transport in the radiation belts. • Radial transport and the role of ULF waves. • Characteristics of ULF waves, MHD simulations • Boundary conditions on radial transport. • Conclusion. S. Elkington, GEM 2003

  3. The outer zone radiation belts • Trapped particles drifting in orbits encircling Earth. • Two spatial populations: inner zone and outer zone. • Energies from ~200 keV to > few MeV S. Elkington, GEM 2003

  4. Particle motion in the radiation belts Trapped particles execute 3 characteristic types of motion: Characteristic time scales: • Gyro: ~ millisecond • Bounce: ~ 0.1-1.0 s • Drift: ~ 1-10 minutes S. Elkington, GEM 2003

  5. Adiabatic invariants • Associated with each motion is a corresponding adiabatic invariant: • Gyro: M=p2/2m0B • Bounce: K • Drift: L • M: perpendicular motion • K: parallel motion • L: radial distance of eq-crossing in a dipole field. If the fields guiding the particle change slowly compared to the characteristic motion, the corresponding invariant is conserved. S. Elkington, GEM 2003

  6. Fluxes in the radiation belts The radiation belts exhibit substantial variation in time: • Storm commencement: minutes • Storm main phase: hours • Storm recovery: days • Solar rotation: 13-27 days • Season: months • Solar cycle: years S. Elkington, GEM 2003

  7. Why study the radiation belts? • Because they’re physically interesting! • Relativistic electrons have been associated with spacecraft ‘anomalies’. Want to try to describe how radiation evolves in time at a given point in space. S. Elkington, GEM 2003

  8. Describing the radiation belts The radiation belts may be completely characterized at a point in time by its distribution function: Also referred to as the phase space density, f gives the number of particles in a volume (x+dx, y+dy, z+dz), with momenta between (px+dpx, py+dpy, pz+dpz ). The flux in a region of space may be related to the distribution function through S. Elkington, GEM 2003

  9. The distribution function and the adiabatic invariants The distribution function may equivalently be written in terms of the invariants and corresponding phase: If the distribution is uniform in phase (e.g. uniform f3a no drift bunching in L), then the phase space density taken at a point may be considered the same at all points corresponding to the same M, K, and L. S. Elkington, GEM 2003

  10. Transport and Fokker-Planck The evolution of the phase space density is given by the Fokker-Planck equation: Sources Coherent terms (e.g. friction) Stochastic terms (e.g. diffusion) Losses For example, to quantify a process that leads only to diffusion in L, we would write S. Elkington, GEM 2003 (M. Schulz, AGU Monograph 97, 1996)

  11. Transport in M, K: local heating S. Elkington, GEM 2003

  12. Whistler mode chorus at dawn combined with EMIC interactions heat and isotropize particles. Leads to transport in M, K, and L. Local heating example:resonant interactions with VLF waves Summers et al. (JGR 103, 20487, 1998) proposed that resonant interactions with VLF waves could heat particles: S. Elkington, GEM 2003

  13. Transport in L: radial transport S. Elkington, GEM 2003

  14. Energization and ULF waves Electron moving in a dipole magnetic field with slowly-varying dawn-dusk potential electric field • fD~mHz … ULF waves! • Only need consider resonant frequencies in analysis: S. Elkington, GEM 2003

  15. …and to radial transport Nonrelativistically, and in a dipole, or so changing energy (W) while conserving M will necessarily lead to transport in L. S. Elkington, GEM 2003

  16. Observed associations between ULF waves and radiation belt activity? • Baker et al., GRL 25, 2975, 1998 • Rostoker, GRL 25, 3701, 1998 • Mathie & Mann, GRL 27, 3621, 2000 • O’brien et al., JGR, 2003, in press. S. Elkington, GEM 2003

  17. Characterizing ULF interactions • Start particles at differing energiesadiffering drift freqs. • Impose waves characterized by particular m, w. • Look max energy gain at Poincare plots: • Plot motion in the phase space coordinates (L,f3), at snapshots in time differing by 1/f. • Particle motion constrained to lines. • Drift resonance appears as ‘island’ at appropriate energy (frequency). S. Elkington, GEM 2003

  18. Higher-order resonances In the outer zone, the m=1 noon-midnight asymmetry leads to additional resonances: S. Elkington, GEM 2003

  19. Multiple frequencies: radial diffusion S. Elkington, GEM 2003

  20. Quantifying effects of diffusion Effect of diffusion on radiation belts can be quantified by solving the diffusion equation with appropriate boundary conditions: To do this, we need to know the appropriate diffusion coefficients… • What are the D0’s? • What is the ULF power? S. Elkington, GEM 2003

  21. Diffusion Characteristics: D0 • Start series of particles at one L. • Let them evolve in a compressed dipole under the influence of a constant P(L,w). • Watch spread of L in time. • Calculate DLL=<dL2>/2t. • Invert to calculate D0. S. Elkington, GEM 2003

  22. Diffusion Characteristics, 09/24-26/1998:constant P, time-varying compression S. Elkington, GEM 2003

  23. Characteristics of ULF waves? • ULF Power • ULF waves: decrease with decreasing L • Decrease with increasing frequency • Depend on solar wind velocity • May or may not have significant local time dependence. Kepko et al., GRL 29(8), 1197, 2002 S. Elkington, GEM 2003

  24. ULF activity in MHD simulations • ULF waves can be described within the framework provided by MHD. • Lyon-Fedder-Mobarry: • Global, 3d • Driven by upstream conditions S. Elkington, GEM 2003

  25. MHD simulations of ULF power, 09/24/1998 • ULF power in MHD shows expected radial, frequency dependence. • Azimuthal dependence: frequently see structure in local time. S. Elkington, GEM 2003

  26. Parametric studies, perturbations • Constant solar wind velocity 600 km/s. • Density perturbations in solar wind at 3 mhZ. • Spectral analysis in magnetosphere shows strong peak at 3 mHz, but also peaks at 5, 7, and 10 mHz. S. Elkington, GEM 2003

  27. Parametric studies, const solar wind • Constant solar wind velocity 600 km/s. • Nothing else! • Indicates that 5, 7 mHz features are due to K-H waves on the flanks. S. Elkington, GEM 2003

  28. Shear waves & particle acceleration • Limited local time: propagating waves dusk and counterpropagating waves dusk still lead to energization. S. Elkington, GEM 2003

  29. Mode structure in ULF simulations • Diffusion coefficients: depend on P(mwD), etc., so must know the power in each specific mode number. Recovery Phase Main Phase S. Elkington, GEM 2003

  30. Energization through radial transport: a plasma sheet source? • Simplistic considerations put r0~20 RE for M corresponding to a 1 MeV geosynchronous electron • Conversely, W for r0=6.6RE is 50 keV. • So is transport/acceleration a viable mechanism at all? N. Tsyganenko http://nssdc.gsfc.nasa.gov/space/model/magnetos/data-based/modeling.html S. Elkington, GEM 2003

  31. Plasmasheet access to inner magnetosphere: observations • Korth et al. [JGR 104, 25047, 1997] found good agreement with theory for keV electrons. • MeV electrons? S. Elkington, GEM 2003

  32. MHD/particle simulations of energetic electron trapping • 60 keV test electrons, constant M. • Started 20 RE downtail, 15s intervals. • Evolves naturally under MHD E and B fields. • Removed from simulation at magnetopause. • Color coded by energy. S. Elkington, GEM 2003

  33. Conclusions/Summary Our understanding of radial transport in the radiation belts is better, but still will require considerable effort. • Transport equations: DLL proportionalities, energy dependence. • ULF waves: • Power spectrum and occurrence characteristics of ULF waves. • Mode structure of magnetospheric waves. • How is power coupled from solar wind to inner magnetosphere? • Boundary conditions: the plasma sheet? • Determine plasmasheet access. • Distribution in plasmasheet. S. Elkington, GEM 2003

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