A New Model of Electron Pitch Angle Distributions and Loss Timescales in the Earth’s Radiation Belts

As the number of satellites on orbit grows it is increasingly important to understand their operating environment. Physics-based models can simulate the behavior of the Earth's radiation belts by solving a Fokker-Planck equation. Three-dimensional models use diffusion coefficients to represent the interactions between electromagnetic waves and the electrons. One-dimensional radial diffusion models neglect the effects of energy diffusion and represent the losses due to the waves with a loss timescale. Both approaches may use pitch angle distributions (PADs) to create boundary conditions, to map observations from low to high equatorial pitch angles and to calculate phase-space density from observations. We present a comprehensive set of consistent PADs and loss timescales for 2 ≤ L* ≤ 7, 100 keV ≤ E ≤ 5 MeV and all levels of geomagnetic activity determined by the Kp index. These are calculated from drift-averaged diffusion coefficients that represent all the VLF waves that typically interact with radiation belt electrons and show good agreement with data. The contribution of individual waves is demonstrated; magnetosonic waves have little effect on loss timescales when lightning-generated whistlers are present, and chorus waves contribute to loss even in low levels of geomagnetic activity. The PADs vary in shape depending on the dominant waves. When chorus is dominant the distributions have little activity dependence, unlike the corresponding loss timescales. Distributions peaked near 90° are formed by plasmaspheric hiss for L* ≤ 3 and E 3 and E > 1 MeV. When hiss dominates, increasing activity broadens the distribution but when EMIC waves dominate increasing activity narrows the distribution.

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