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

We have simulated radial diffusion of mirroring relativistic electrons in the outer radiation caused by a broadband spectrum of waves that cover resonant frequencies of 3-5 mHz (Pc5) with a large marginal. A time-varying phase of each Fourier mode is necessary for generation of diffusive response in particles. Simulation results vary significantly, where in one example for a flat spectrum the diffusion coefficient averaged over 20 simulations is DLL = 3.94±2.72 10-2 h-1. We also investigate diffusion of particles that are not within the resonant frequency band. We show through normalizing the spectral power that the peak electric field amplitude in a spectrum is the dominating factor in the diffusion rate for this case. An inverse power-law, a, with increasing values causes an increase in diffusion rate. Both theory and particle tracing simulations show that the diffusion rate increases exponentially by a factor of 5000 from the flat spectrum (a=0) up to a steep power law of a=1.6 where the rate stagnates. An enhanced transport mechanism is demonstrated by which particles interact with distinct modes coexisting with low amplitude noise background. Resonant particles are transported radially depending on wave amplitudes and frequency adjacency. With coexisting noise some particles can diffusive away from the influential reach of the modes when being close to the outer radial limits, thus additional scattering occurs. By comparing an environment with only noise with another that in addition contains two distinct Chirikov fulfilling modes the standard deviation of radial location of particle population is shown to differ by a maximal factor of 2-6 times depending on the diffusion rate. Finally we simulate particle transport in realistic MHD fields for particular events where ULF activities have been identified. The diffusive behavior is mapped for both original fields and for scenarios where the spectral profiles have been altered to fit ideal specifications as discussed earlier.