Equatorial Pitch Angle Distributions of 1–50 keV Electrons in Earth's Inner Magnetosphere: An Empirical Model Based on the Van Allen Probes Observations

Using 7 years of data from the Helium, Oxygen, Proton, and Electron instrument on the Van Allen Probes, equatorial pitch angle distributions (PADs) of 1–50 keV electrons in Earth's inner magnetosphere are investigated statistically. An empirical model of electron equatorial PADs as a function of radial distance, magnetic local time, geomagnetic activity, and electron energy is constructed using the method of Legendre polynomial fitting. Model results show that most equatorial PADs of 1–10s of keV electrons in Earth's inner magnetosphere are pancake PADs, and the lack of butterfly PADs is likely due to their relatively flat or positive flux radial gradients at higher altitudes. During geomagnetically quiet times, more anisotropic distributions of 1–10s of keV electrons at dayside than nightside are observed, which could be responsible for moderate chorus wave activities at dayside during quiet times as reported by previous studies. During active times, the anisotropy of 1–10s of keV electrons significantly enhances, consistent with the enhanced chorus wave activity during active times and suggesting the critical role of 1–10s of keV electrons in generating chorus waves in Earth's inner magnetosphere. Different enhanced anisotropy patterns of different energy electrons are also observed during active times: at R > ∼4 RE, keV electrons are more anisotropic at dawn to noon, while 10s of keV electrons have larger anisotropy at midnight to dawn. These differences, combined with the statistical distribution of chorus waves shown in previous studies, suggest the differential roles of electrons with different energies in generating chorus waves with different properties.