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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]

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Wave-Particle Interaction

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Diffusion Coefficient

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Geometry of Interaction with Wave Packet

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Trajectories in Velocity Space

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Whistler-Mode Instability f(p , p || ) = g(E) sin 2s ; s = anisotropy s > 0 Im > 0 for / < s/(s+1) resonance with growing wave for electrons with E > E * = (B 0 2 /8 N 0 s)(s+1) 2 (This was a nonrelativistic calculation.)

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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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