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Yeh & Hill 1981
Yeh, H.-C. and Hill, T.W. (1981). Mechanism of parallel electric fields inferred from observations. Journal of Geophysical Research 86: doi: 10.1029/JA086iA08p06706. issn: 0148-0227.

An analysis of satellite data from regions of upward Birkeland (magnetic-field-aligned) current shows that the typical magnetic-field-aligned potential drop in the auroral zone is larger than required to provide direct acceleration of magnetospheric electrons by the field-aligned electric field against the upward magnetic force to produce the observed upward Birkeland current. A model of simple electrostatic acceleration without anomalous resistivity predicts observable relations between parallel current and parallel potential drop and between energy deposition and parallel potential drop. The temperature, density, and species of the unaccelerated charge carriers are the relevant parameters of the model. Simultaneously measurements of electron precipitation and ion drift velocities on the satellites Atmosphere Explorere C and D were used to test these relations. In a steady state the divergence of ionospheric currents must be compensated by Birkeland currents. The model current-voltage relation was applied to predict the densities of the primary charge carriers (i.e., plasma sheet electrons above the acceleration region for upward currents). In cases involving thin arc structures, where the reliable estimation of the divergence of ionospheric current is difficult and the steady-state assumption may not apply, the precipitating energy flux versus voltage relation was used to predict the densities of the unaccelerated plasma sheet electrons. Within the experimental uncertainties, reasonable agreement is found between these predicted densities and those inferred directly from the simultaneous data of the Low-Energy Electron Experiment. These results are interpreted as indicating that anomalous resistivity is not important in determining the magnitude of the field-aligned potential drop in the auroral zone.

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Journal of Geophysical Research
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