Stochastic Simulations of Radiation Belt Relativistic Wave-Particle Interactions

Abstract

Radial diffusion has been considered a primary transport and energization mechanism in Earth's radiation belts since soon after its discovery in 1958. Although its validity remains an open question, it is incorporated into many radiation belt models. Radiation belt particles are characterized by three periodic motions—gyro, bounce, and drift—each associated with an adiabatic invariant. Radial diffusion requires violating the drift invariant via ultra low-frequency (ULF) wave-particle interactions (WPIs). This thesis investigates relativistic guiding-center ULF-WPIs in Earth's equatorial dipole field through complementary numerical simulations and theoretical derivations. Both electric (derivable from a scalar potential) and electromagnetic (derivable from a vector potential) WPIs are considered. First, deterministic single-mode ULF-WPIs are analyzed using Poincaré plots whose numerical island half-widths agree with theory. Then, diffusive WPIs are simulated, and resulting numerical diffusion coefficients agree with theory. We also consider perturbations similar to those described in Fälthammar (1965), a foundational work on the topic. While agreement is obtained for the electric part, a discrepancy is found for the electromagnetic part due to an assumption made in his work and when modified, agreement is achieved. Next, multimode ULF-WPIs are examined. First, the wave perturbations are analyzed and the "effective correlation" is developed. Then, we explore three wave parameters: The spectrum frequency width, spacing, and amplitude. We find that the decorrelation time of the system is inversely proportional to the spectrum width. A wide spectrum width, a narrow spectrum spacing, and an intermediate amplitude are required to achieve a quasilinear diffusive interaction. Poincaré island overlap ratios are simultaneously tracked to determine lower and upper bounds of the quasilinear diffusive region.

Radiation belt dynamics includes other WPIs spanning timescales from milliseconds to minutes, complicating their incorporation in a single simulation using conventional methods. We present results from a separate computational model, K2, simulating the March 17, 2013 geomagnetic event. The model combines a magnetohydrodynamic (MHD)-particle framework (incorporating ULF processes) with stochastic differential equation (SDE) methods that incorporate chorus wave processes. Furthermore, nonlinear effects (e.g., phase trapping and bunching) are also incorporated in K2, and the results are interpolated along spacecraft trajectories where significant under-sampling arises.