Modeling for precipitation loss of ring current protons by electromagnetic ion cyclotron waves

We examine the precipitation loss of ring current protons produced by the electromagnetic ion cyclotron (EMIC) waves at the location L  =3.5 where the symmetrical ring current primarily occurs. Using a recently introduced hybrid finite difference (HFD) method, we solve the standard Fokker–Planck diffusion equation with incorporation of the cross diffusion terms that were often ignored in the previous work. We show that EMIC waves can produce efficient pitch angle scattering of energetic (tens of keV) protons, yielding a rapid decrement in the flux with a time scale of a few hours, consistent with observational data. We also demonstrate that omission of the cross diffusion terms generally overestimates the decrement in the flux, typically by a factor of ∼2∼2 after a few hours at lower pitch angles, suggesting that the cross terms also play an important role in precipitation loss of ring current protons.