Spectra of keV protons related to ion-cyclotron wave packets

We use the Fokker-Planck-Kolmogorov equation to study the statistical aspects of stochastic dynamics of the radiation belt (RB) protons driven by nonlinear electromagnetic ion-cyclotron (EMIC) wave packets. We obtain the spectra of keV protons scattered by these waves that show steeping near the gyroresonance, the signature of resonant wave-particle interaction that cannot be described by a simple power law. The most likely mechanism for proton precipitation events in RBs is shown to be nonlinear wave-particle interaction, namely, the scattering of RB protons into the loss cone by EMIC waves.