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

Wave-Particle Interaction

Diffusion Coefficient

Geometry of Interaction with Wave Packet

Trajectories in Velocity Space

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.)

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).