Comparison of Energetic Electron Distribution Functions Derived from CXDs (L~4.2), CPAs and SOPAs (L~6.6), and Model AE8 at or near the Magnetic Equator

Abstract:

Throughout the range of L-shells important for GPS and GEO spacecraft (4.2<L<7.2) the energy dependence of the electron distribution function derived from model AE8 is represented very well by a sum of 3 exponential components, soft, hard, and tail, each parameterized by a temperature and a density. Furthermore, the 3 temperatures vary only slightly over this range of L-shells suggesting an almost isothermal electron population. Indeed, for AE8, the temperatures of the soft and hard populations actually decrease with decreasing L. The event-dominated and non-event-dominated natures of time variations on L-shells observed by GPS and GEO, respectively, underlie this paradox.¹ At one end of the L range, and consistent with AE8, in situ measurements (averaged for several minutes or more) from GEO spacecraft are represented well by sums of 3 exponential components, and individual spectra resemble their average. At the lower end of the L range, however, individual CXD spectra exhibit characteristic non-equilibrium leakage features,² and they bare little resemblance to their average. Local-time asymmetries develop at L=4.2 during event decay phases that follow electron injections; 0.3 MeV electrons exhibit the largest asymmetries on these L-shells. When a 14-day-long averaging interval (sets of 14 individual CXD spectra with similar magnetic-equator-crossing coordinates) includes one or more electron injections, the energy dependence of the average spectra often resemble sums of 3 exponential components, consistent with the model based on average fluxes, AE8.

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2.) J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis, John Wiley, New York, 1976, pp.381-383.