title: Radial Diffusion Models of Earth’s Outer Radiation Belt using Stochastic Parameterizations
Creators: name: Thompson, Rhys
Publisher: name: University of Reading
Year: 2021

description: Earth’s outer radiation belt is very dynamic and contains high-energy particles which are hazardous to spacecraft. Radial diffusion is the process by which energetic electrons undergo bulk transport and energization, driven by interactions with ultralow frequency (ULF) waves. Modelled by a Fokker-Planck equation, all of the physics to describe the strength of radial diffusion is contained in the radial diffusion coefficient, DLL, typically modelled proportionally to ULF wave power as a function of electron drift-shell (L ∗ ) and geomagnetic activity. A number of parameterizations for DLL exist but can vary by orders of magnitude. State of the art radial diffusion coefficient models therefore carry great uncertainty. All modern DLL parameterizations are deterministic and based on median ULF wave power spectral density. In this Thesis we investigate the impact on radial diffusion when DLL is modelled as an ensemble which encompasses the probabilistic distribution of ULF wave power. The underlying factors which contribute to variability in ULF wave power distributions are extensive and we concentrate on three of the largest: the variability of L ∗ with an observation’s location when mapping ULF wave power to adiabatic space, the shape of ULF wave power distributions as measured on board spacecraft as a function of L ∗ , local time and ULF wave frequency, and finally the mapping of ground-based magnetic wave power to space-based electric field power to infer a key component of DLL. We find that L ∗ varies in physical space significantly as a function of magnetic field model and geomagnetic activity, with uncertainties between magnetic field models unable to be completely mitigated. Further, shapes of space-based power approximations are either log-symmetric or log-skewed when separated into L ∗ and wave frequency, although there are characteristic differences across local time. Finally, we find that while mapping ground-based power with a stochastic ULF wave resonance width better aligns with space-based power distributions compared to the state-of-the-art analytic mapping, stochastic parameterizations of other key wave parameters are necessary to recover the full distribution. Combining the sources of variability which quantify the ULF wave power distributions into a stochastically parameterized DLL, we model an ensemble of radial diffusion and compare with a number of deterministic radial diffusion coefficients. In most cases a stochastic DLL results in more diffusion, with the spread of resulting phase space densities in the ensemble rarely enclosing those from the deterministic parameterizations. In addition, ensembles are collectively more diffusive when DLL is sampled more frequently in time and on shorter scale-lengths in L∗. Overall, this thesis demonstrates the importance of variability for impacting rates of radial transport. Future work could extend the stochastic approaches used to here to account for yet to be determined spatio-temporal ULF wave power variability.