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Energy Spectrum Constraints in Radiation Belts: Wave-Particle Interactions

Explore the limiting energy spectrum of a saturated radiation belt due to wave-particle interactions, diffusion coefficients, and velocity space geometry. Resonance conditions for electron waves are examined with anisotropy implications. Study by Schulz and Davidson (1988).

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Energy Spectrum Constraints in Radiation Belts: Wave-Particle Interactions

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  1. Limiting Energy Spectrum of a Saturated Radiation Belt Michael Schulz 1037 Twin Oak Court Redwood City, CA 94061 (USA) from Schulz and Davidson [JGR, 93, 59-76, 1988]

  2. Wave-Particle Interaction

  3. Diffusion Coefficient

  4. Geometry of Interaction with Wave Packet

  5. Trajectories in Velocity Space

  6. Whistler-Mode Instability f(p, p||) = g(E) sin2s ; s = anisotropy s > 0  Im  > 0 for / < s/(s+1)  resonance with growing wave for electrons with E > E* = (B02/8N0s)(s+1)2 (This was a nonrelativistic calculation.)

  7. Background • Actual (net) instability requires that the path-integrated wave growth rate exceed ln (1/R) ~ 3, which expresses the loss on reflection at wave turning points. • Kennel and Petschek [JGR, 1966] assumed a fixed anisotropy (s) and a fixed spectral form for g(E). They estimated the maximum normalization for g(E) consistent with net wave stability at all frequencies. • Schulz and Davidson [JGR, 1988] also assumed a fixed anisotropy (s) but calculated the electron energy spectrum consistent with net marginal stability for all wave frequencies such that / < s/(s+1).

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