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Stamnes & Rees 1983
Stamnes, K. and Rees, M.H. (1983). Heating of thermal ionospheric electrons by suprathermal electrons. Geophysical Research Letters 10: doi: 10.1029/GL010i004p00309. issn: 0094-8276.

Several investigators have computed ionospheric electron heating rates in the past using an incorrect term in the expression for the energy transfer from the suprathermal to the thermal electrons derived by Mantas [1975>. This incorrect formulation was also based on an electron energy loss rate inversely proportional to the suprathermal electron energy, limiting its application to energies above about 2-3 eV. Since the proper low-energy cutoff is the cross-over energy at which the thermal electron intensity equals the suprathermal one, a considerable portion of the ambient electron heating may take place below 2-3 eV, depending on the ionospheric conditions. Mantas [1981> has amended these inadequacies, but has not explored their geophysical consequences. Comparing electron heating rates and electron temperatures computed by the incorrect approach with identical computations based on the proper energy transfer term, energy loss rate and cross-over energy, we find that the previous approach lends to a substantial underestimate of the ambient electron heating rate as well as the resulting ionospheric electron temperature. This underestimate is more pronounced for solar minimum than for solar maximum conditions as could be anticipated since the elevated electron densities and temperatures at solar maximum lead to a higher cross-over energy and thus a lesser impact of the inadequacies in previous treatments.

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Geophysical Research Letters
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