Field-aligned current (FAC) is here defined by 4&pgr;j=&agr;B, where &agr; is constant along a magnetic field line. The upper limit value of &agr; in the polar magnetosphere, possible source regions of the strongest FAC and the relationship of them to some auroral and ionospheric irregularity cross-field scale sizes are discussed. Cross-field dimensions of the strongest FAC are related to the gyroradii of source particles (O+, He++, He+, H+, e) in the current-generating region. It is suggested that experimental determination, and mapping of the values of &agr;, may assist with the search for the generators of such currents in near-Earth space including in the nearby solar wind. We associate the upper limit of &agr; with the breakup of FAC systems. ¿American Geophysical Union 1991