Simulations and analysis of relativistic electron energization by ULF waves in the Radiation Belts

We present results of guiding-center simulations of relativistic electron transport on the equatorial plane of a compressed-dipole field. We compare harmonically varying wave fields, which produce drift resonances, with random impulses of power-law spectra, which lead to diffusive scattering, both in the frequency range of 3-5 mHz (Pc5). First we measure the effectiveness of individual electrostatic waves with overlapping frequencies in energizing the electron distribution. Azimuthally-polarized waves are 4-8 times more effective in energizing electrons than radially-polarized waves of the same amplitude. An additional constant radial drift of the electrons is observed for waves with a polarization at an angle in the plane between r and φ. When self-consistent wave B-fields are included, we show that resonance widths change drastically. We summarize these cases by writing the energy gain or loss analytically in closed form. We then compare the waves described above with random electric impulses Eφ with power-law spectra for ω >> ωd. In a symmetric-dipole field such random-impulse fields produce a standard diffusive transport which scales as DLL ~ L^6. Compressing the dipole by Bc = 30 nT further increases DLL so that in the vicinity of the geosynchronous orbit the increase is a factor of about 6. When we combine waves and random impulses in the same simulation, we observe enhanced transport near the separatrix regions of resonance islands and electron heating farther away from the islands, while the rate of diffusion remains unaffected. We report the scaling of the radial transport and heating as functions of the spectral power-law and amplitude.