Via NASA Electric Currents from Space (Hat tip: Anaconda)
When in 1973 the navy satellite Triad (see history) flew through this region in a low-altitude orbit, its magnetometer indeed detected the signatures of two large sheets of electric current, one coming down on the morning side of the auroral zone, one going up on the evening side, as expected. Because Kristian Birkeland had proposed long before currents which linked Earth and space in this fashion, they were named Birkeland currents (by Schield, Dessler and Freeman, in a 1969 article predicting some of the features observed by Triad). Typically, each sheet carries a million amperes or more.1 million amperes or more? Nope, no mass there...LOL.
Potemra, T.A., Observation of Birkeland Currents with the TRIAD Satellite, Astrophysics and Space Science, Volume 58, Number 1, Pages 207-226, Sep 1978