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/sub parallel/) and energy flux (epsilon) 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 1very-much-less-thaneV/E/sub 0parallel/very-much-less-than500, epsilon is nearly proportional to V2, and J/sub parallel/ is proportional to V (E/sub 0parallel/ is the parallel thermal energy of the electrons; in the plasmasheet, E/sub 0parallel/=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 kVvery-much-less-thanVvery-much-less-than100 kV). The ohmic-like behavior of an auroral magnetic flux tube (J/sub parallel/proportionalV) and the constancy of epsilon/V2 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(=epsilon/sub obs//V/sub obs/2) to the auroral electron density and temperature in the source region