Analytic description of the electron temperature behavior in the upper ionosphere and plasmasphere

Approximate analytic solutions to the well-known and commonly used time-dependent electron energy balance equation for the upper ionosphere and plasmasphere have been obtained and are discussed. The various potential heating sources for the terrestrial plasmasphere are summarized and the corresponding electron temperatures and related characteristic heating and cooling times are calculated. A comparison between the analytic expressions for the temperature variations and relevant measurements shows excellent agreement.