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Atkinson 1986
Atkinson, G. (1986). Verification of quantitative relationship among Birkeland current sheet motion, intensity, and convective velocity, and also of criterion for expansion onset. Journal of Geophysical Research 91: doi: 10.1029/JA091iA08p08929. issn: 0148-0227.

In this paper, 14 substorms are used to verify the conclusions of an earlier paper on current sheet motions. These conclusions can be summarized as follows: (1) The quantitative relationship VN=VCN -kVI is valid when applied to the upward current sheet in the premidnight quadrant except during the expansion and early recovery phases of substorms (ViN and VCN are the components, normal to the sheet, of the sheet velocity and the convection velocity, kv is a constant, and I is the current sheet intensity). (2) At the time of local northward expansion of the auroras there appears to be a decrease by 1 order of magnitude of the amount of plasma on the flux tubes. (3) The time of initiation of local northward expansion occurs when VCN=kVI. A few additional points emerge from this study: The above relationships are not valid at stations east of the location of initial onset of expansion, and the amount of plasma on flux tubes tends to return to its preexpansion value after a substorm. Further conclusions are (1) that the physical mechanism responsible for the northward expansion in a westward traveling surge is the same as in the initial near-midnight expansion, (2) that the triggering of expansion occurs just as the tail begins to recede away from the earth, and (3) that the apparent decrease in plasma content is consistent with the formation of a near-earth neutral line; however, it could also result from the breakdown of the sheet approximation for the currents.

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Journal
Journal of Geophysical Research
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American Geophysical Union
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