Limiting Particle Flux in a Planetary Radiation Belt

We determined the Kennel-Petschek limiting electron flux in a planetary radiation belt in a fully relativistic regime, without assuming a pre-determined form for the particle energy distribution. The limiting flux is determined by a steady-state marginal stability criterion in which a convective wave gain condition is applied over all frequencies for which wave growth occurs. This condition produces an integral equation for the trapped flux. We find that in the relativistic regime the limiting electron energy spectrum varies asymptotically as 1/E, for large energy E, just as in the non-relativistic case. However, the scaling coefficient in the relativistic case is twice that in the non-relativistic result. We compare numerical solutions for the limiting spectra with measured energetic electron spectra at Jupiter.