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 (&egr;) 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/E0∥≪500, &egr; is nearly proportional to V2, and J∥ is proportional to V (E0∥ is the parallel thermal energy of the electrons; in the plasmasheet, E0∥=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 &egr;/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(=&egr;obs/Vobs2) to the auroral electron density and temperature in the source region (i.e., in the plasmasheet).