Parametric Study of ULF Wave Spectra and Particle Diffusion in the Radiation Belts

One of the main mechanisms thought to induce relativistic electron transport and energization in the radiation belt is radial diffusion through interaction with broadband spectra of electromagnetic wave fields. Studies by other research groups have emphasized a correlation between power spectral density and the diffusion coefficient DLL. However the main focus has been on particles interacting resonantly with stationary and ergodic fields where the internal phases are fixed. We propose an analytical function for the diffusion coefficient with an important factor being the introduction of phases that are set to be randomized at fixed time intervals. The calculated diffusion rates are verified through the use of a guiding center test particle code. For a comparison of the results between the analytical function and the test particle code simplified wave fields of m=0 are assigned into azimuthally limited sectors and randomized at fixed intervals. The electrons in the particle tracing code do interact resonantly with the specifically assigned spectra from which resulting diffusion coefficients become higher than for the analytically calculated values of non-resonant interaction. The plotted results suggest that resonant contribution is between 1.5-3.5 times larger than the non-resonant depending on reset rate and harmonic interaction. Should the rate of phase randomization exceed the drift frequency of the electrons the resonant interactions would diminish where only non-resonant diffusion still occurs. Furthermore we show the transition from narrowband to broadband spectra, as well as cases containing both. We will discuss the outcome from varied power law profiles in the spectrum, as well as the difference between using a symmetric and an asymmetric magnetic dipole field. The initial energies and radial placement of the electrons determine their adiabatic invariants which in turn affects the diffusion coefficient. For our setup, where a simplified electrostatic spectrum of m=0 was used, the coefficient was found to be DLL ~ L^7.3 in a symmetric dipole field and DLL ~ L^14.9 in an asymmetric dipole. These values are higher than what have been derived in earlier studies for m>0 and stationary phases.