Relationship between auroral electrons fluxes and field aligned electric potential difference

A kinetic theory is used to model the field‐aligned distribution of auroral electrons along dipole magnetic field lines. Analytical formulae are obtained for the particle flux ( J ∥ ) and energy flux (ε) as functions of V , the electric potential difference between the equatorial source region and the ionosphere where the accelerated electrons are precipitated and detected by rocket instrumentation. For 1 ≪ eV/E o( ≪500, ε is nearly proportional to V ², and J ) is proportional to V ( E o) is the parallel thermal energy of the electrons; in the plasmasheet, E o( =0.2–0.6 keV). The observed values for the field‐aligned potential drop ( V ) usually range within the limits defined by this double inequality (i.e., 0.6 kV ≪ V ≪100 kV). The ohmic‐ like behavior of an auroral magnetic flux tube ( J ) ∝ V ) and the constancy of ε/ V ² has been found experimentally by Lyons et al. (1979). Using an asymptotic expansion for the kinetic electron precipitation flux and energy flux we have obtained a useful formula which relates the Lyons‐Evans‐Lundin constant K (=ε obs / V obs ²) to the auroral electron density and temperature in the source region (i.e., in the plasmasheet).