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In the last years, electron density profile functions characterized by a linear dependence on the scale height showed good results when approximating the topside ionosphere. The performance above 800 km, however, is not yet well investigated.
This study investigates the capability of the semi-Epstein functions to represent electron density profiles from the peak height up to 20,000 km. Electron density observations recorded by the Van Allen Probes were used to resolve the scale height dependence in the plasmasphere.
It was found that the linear dependence of the scale height in the topside ionosphere cannot be directly used to extrapolate profiles above 800 km.
We find that the dependence of scale heights on altitude is quadratic in the plasmasphere. A statistical model of the scale heights is therefore proposed. After combining the topside ionosphere and plasmasphere by a unified model, we have obtained good estimations not only in the profile shapes, but also in the Total Electron Content magnitude and distributions when compared to actual measurements from 2013, 2014, 2016 and 2017.
Our investigation shows that Van Allen Probes can be merged to radio-occultation data to properly represent the upper ionosphere and plasmasphere by means of a semi-Epstein function.
The Cluster mission has produced a large data set of electron flux measurements in the Earth's magnetosphere since its launch in late 2000. Electron fluxes are measured using Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector as a function of energy, pitch angle, spacecraft position, and time. However, no adiabatic invariants have been calculated for Cluster so far. In this paper we present a step-by-step guide to calculations of adiabatic invariants and conversion of the electron flux to phase space density (PSD) in these coordinates. The electron flux is measured in two RAPID/IES energy channels providing pitch angle distribution at energies 39.2-50.5 and 68.1-94.5 keV in nominal mode since 2004. A fitting method allows to expand the conversion of the differential fluxes to the range from 40 to 150 keV. Best data coverage for phase space density in adiabatic invariant coordinates can be obtained for values of second adiabatic invariant, K, similar to 10(2), and values of the first adiabatic invariant mu in the range approximate to 5-20 MeV/G. Furthermore, we describe the production of a new data product "LSTAR," equivalent to the third adiabatic invariant, available through the Cluster Science Archive for years 2001-2018 with 1-min resolution. The produced data set adds to the availability of observations in Earth's radiation belts region and can be used for long-term statistical purposes.