Resonance broadening effects of weak turbulence on Earth's radiation belt electrons

The quasilinear diffusion theory is generalized to include the resonance broadening effect of weak turbulence on relativistic electrons in Earth's radiation belts. In contrast with quasilinear resonant diffusion, in which cases the resonant condition should be rigorously satisfied, the second-order theory demonstrates that the wave-driven scattering of relativistic electrons could be broadened into an area of velocity space adjacent to the resonant region. It is shown that a finite departure time, resulted from the second-order wave-particle interaction, is the key factor controlling the occurrence and effectiveness of such a resonance broadening. The formula to solve the departure time has been proposed. Adopting the solved departure time, the resultant model can correctly reproduce results of test particle simulations. Our result indicates the importance of resonance broadening effect in the radiation belt modeling, and in understanding the weak turbulence dynamics in a magnetized plasma system.