Magnetic field‐aligned electric field acceleration and the characteristics of the optical aurora

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Abstract
The long‐recognized association of brighter aurora with more deeply penetrating, and hence more energetic electrons is examined. Using the Knight (1973) relation between the magnetic field aligned current density j∥ and potential drop V∥, derived from the theory of single particle motion in the presence of a magnetic field‐aligned electric field, an approximate expression relating the energy flux Q of the precipitating electrons over discrete aurora and the mean particle energy EM is derived: Q(ergs/cm² s) = kEMγ, where 1.5 ≤ γ ≤ 2 and k depends on the temperature and density of the plasma in the source region. This expression is used in conjunction with an auroral optical excitation and emission model to specify the dependence of the red (O I[630.0])/blue (N2+(427.8)) ratio of auroral optical emissions on the brightness of the aurora. It is shown that the quantitative predictions of the discrete auroral theory are in accord with observations of the aurora. Thus the often observed anticorrelation of the red/blue ratio with auroral brightness is consistent with the single‐particle motion theory. It follows that in discrete auroral events where the theory is valid, the brightening of the aurora involves an increase in both the mean energy and the number flux of precipitating electrons.