  Recently, we showed that the self-field transport critical current, Ic(sf),
of a superconducting wire can be defined in a more fundamental way than the
conventional (and arbitrary) electric field criterion, Ec = 1 microV/cm. We
defined Ic(sf) as the threshold current, Ic,B, at which the perpendicular
component of the local magnetic flux density, measured at any point on the
surface of a high-temperature superconducting tape, abruptly crosses over from
a non-linear to a linear dependence with increasing transport current. This
effect results from the current distribution across the tape width
progressively transitioning from non-uniform to uniform. The completion of this
progressive transition was found to be singular. It coincides with the first
discernible onset of dissipation and immediately precedes the formation of a
measureable electric field. Here, we show that the same Ic,B definition of
critical currents applies in the presence of an external applied magnetic
field. In all experimental data presented here Ic,B is found to be
significantly (10-30%) lower than Ic,E determined by the common electric field
criterion of Ec = 1 microV/cm, and Ec to be up to 50 times lower at Ic,B than
at Ic,E.
