By Clare Watt (Northumbria University)
Our work here combines observations and ensemble numerical simulations to study the effect of temporal variability in radiation belt physics. Kinetic wave-particle interactions in Earth’s outer radiation belt are an effective way to energize and scatter high-energy electrons. A Fokker-Planck equation is often used to model the wave-particle interactions, and we studied the way it responds to the temporal variation of the quasi-linear diffusion coefficient in the case of pitch-angle diffusion due to plasmaspheric hiss. We used stochastic parameterisation [Berner et al., 2017] to describe the temporal evolution of hiss diffusion coefficients in ensemble numerical experiments, guided throughout by observations of wave activity and plasma parameters from the NASA Van Allen Probes. Ensemble solutions of the Fokker-Planck equation depend significantly on the timescale of variation, varied here between minutes and hours. We analysed timescales over which it is useful to construct diffusion coefficients and conclude that there is a useful maximum averaging timescale that should be used to construct a diffusion coefficient from observations. This timescale is likely less than the orbital period of most inner magnetospheric missions. Although arithmetic averaging of inputs to diffusion coefficients is not recommended [Watt et al., 2019], arithmetic drift-averaging of the diffusion coefficients themselves can be appropriate in some cases. We found that in some locations, rare but large values of the diffusion coefficient occur during periods of relatively low number density. Ensemble solutions are sensitive to the presence of these rare values, supporting the need for accurate cold plasma density models in radiation belt descriptions.
Figure 1: Ensemble results for numerical diffusion experiments using Dαα(L* = 3). Each panel shows a column-normalised probability distribution function for the phase space density f just outside the loss-cone αLC for (A) Δt = 2 min, (B) Δt = 10 min, (C) Δt = 30 min, (D) Δt = 2 h, (E) Δt = 4 h, and (F) Δt = 6 h. Note that each histogram is displayed using the same vertical binning, giving the histograms a pixelated appearance.
Berner, J., et al. (2017) Stochastic parameterization: towards a new view of weather and climate models. Bulletin of the American Meteorological Society, 98 (3). pp. 565-588. ISSN 1520-0477 doi: https://doi.org/10.1175/BAMS-D-15-00268.1
Watt, C. E. J., Allison, H. J., Meredith, N. P., Thompson, R. L., Bentley, S. N., Rae, I. J., et al. (2019). Variability of quasilinear diffusion coefficients for plasmaspheric hiss. J. Geophys. Res. Space Phys. 124, 8488–8506. doi:10.1029/2018ja026401
Watt, C. E. J., Allison, H. J., Bentley, S. N., Thompson, R. L., Rae, I. J., Allanson, O., … Killey, S. (2022). Temporal variability of quasi-linear pitch-angle diffusion. Frontiers in Astronomy and Space Sciences. https://www.frontiersin.org/articles/10.3389/fspas.2022.1004634