Stability of High- ${\rm J}_{\rm c}$ ${\rm Nb}_{3}{\rm Sn}$ Wires in the Adiabatic Limit

High-J_c Nb₃Sn strands often exhibit instabilities in 4.2 K liquid helium at low fields ~ 0.5 to 3 T which are associated with magnetization flux-jumps. However at 1.9 K in superfluid helium, a minimum in premature quench currents at intermediate fields of 5 to 7 T has been observed in voltage-current measurements. These measurements are typically used for critical current determinations, and the premature quenching is driven by current redistribution within the strand as the current is increased and is termed “self-field” instability. In this paper, the magnetization and self-field stability of Nb₃Sn strands with J_c ~ 2000 A/mm² at 12 T are described for a series of wires made using the Sn-tube approach with filament diameters ranging from 13 to 65 μm. The copper stabilizer of these wires after reaction has residual resistivity ratio, RRR, of ~5, which in effect means that any dynamic stabilization from thermal conduction effects is negligible. In this regime of RRR, we find that the magnetization stability with transport current increases with decreasing filament diameter as predicted by simple adiabatic theory. We also observed that at 4.2 K the self-field stability improved with decreasing filament size, but became worse with decreasing temperature as seen in measurements at 2.0 K.