By Rhys Thompson (University of Reading)
The Van Allen outer radiation belt is a region in near‐Earth space containing mostly high‐energy electrons trapped by the Earth's geomagnetic field. It is a region populated by satellites that are vulnerable to damage from the high‐energy environment. Many modern outer radiation belt models simulate the long‐time behaviour of high‐energy electrons by solving a three‐dimensional Fokker‐Planck equation for the drift‐ and bounce‐averaged electron phase space density that includes radial, pitch‐angle, and energy diffusion.
Radial diffusion is an important process, driven by ultralow frequency (ULF) waves, where electrons are drawn from the outer boundary and accelerated toward Earth, or pushed away from the outer radiation belt and lost to interplanetary space. All of the physics is contained in the radial diffusion coefficient, DLL, often deterministically parameterized to providea single output from the specified inputs which does not allow for any variability in the underlying ULF wave power.
We perform idealized numerical ensemble experiments on radial diffusion, introducing temporal and spatial variability to a widely used DLL, based on the median of statistical ultralow frequency (ULF) wave power for a particular geomagnetic index Kp, through stochastic parameterization constrained by statistical properties of its underlying observations. Results for one of the experiments is shown below in Figure 1. Our results demonstrate the sensitivity of radial diffusion over a long time period to the full distribution of the radial diffusion coefficient, highlighting that information is lost when only using median ULF wave power. A better understanding of temporal and spatial variations of ULF wave interactions with electrons, and being able to characterize these variations to a good level of accuracy, is vital to produce a robust description of radial diffusion over long timescales in the outer radiation belt.
Figure 1: Ensemble results for the electron phase space density (PSD) at the end of a 2 day radial diffusion experiment, where ensemble DLL time series over the duration of the experiment are formulated by applying (lognormal) variability to a constant deterministic DLL (Kp=3) over a range of temporal variability scales (1, 3, 6, 12, and 24 hr, respectively). When variability is applied it persists until to the next hour of variability (relative to the temporal variability scale) where the process is repeated. The median (dashed), mean (dash‐dot) ensemble profiles are shown, as well as the initial PSD profile (dotted) and the deterministic solution with constant deterministic DLL (solid). Ensemble kernel density estimates of the resulting electron PSD are also shown.
Please see the paper for full details:
, 2020). Accounting for variability in ULF wave radial diffusion models. Journal of Geophysical Research: Space Physics, 125, e2019JA027254. , & (https://doi.org/10.1029/2019JA027254