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Rothwell et al. 1984
Rothwell, P.L., Silevitch, M.B. and Block, L.B. (1984). A model for the propagation of the westward traveling surge. Journal of Geophysical Research 89: doi: 10.1029/JA080i010p08941. issn: 0148-0227.

A unified model is developed for the propagation of the westward traveling surge (WTS) that can explain the diversity in the observed surge characteristics. We start with the Inhester--Baumjohann model for the surge region, which implicitly includes both the Hall and Pedersen currents. It is found that precipitating electrons at the conductivity gradient modify the gradient, causing it to propagate as a wave front. The velocity of propagation is directly dependent on the ionization efficiency of the precipitating electrons and therefore increases dramatically when they become more energetic during substorm onsets. For example, we predict that when the incident electron energy changes from 1 keV to 10 keV the surge velocity should increase from 2 km/s to 34 km/s. The direction of the surge motion depends on the presence of polarizaton charges on the poleward surge boundary. This is related to the efficiency with which the poleward ionospheric currents are closed off into the magnetostphere by the field-aligned currents. Inclusion of the electron-ion recombination rate modifies the surge propagation velocity and leads to explicit expressions for the conductivity profile. Sufficient precipitation current is required to overcome electron--ion recombination in order for the surge to expand. When the precipitating current is less than this threshold the WTS retreats. Therefore, the model describes the ionospheric response to both the expansion and recovery phases of the magnetic substorm.

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Journal of Geophysical Research
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