Suppression of flux jumps in high-$J_c$ Nb$_3$Sn conductors by ferromagnetic layer

Flux jumps observed in high-$J_c$ Nb$_3$Sn conductors are urgent problems to construct high field superconducting magnets. The low-field instabilities usually reduce the current-carrying capability and thus cause the premature quench of Nb$_3$Sn coils at low magnetic field. In this paper, we explore suppressing the flux jumps by ferromagnetic (FM) layer. Firstly, we experimentally and theoretically investigate the flux jumps of Nb$_3$Sn/FM hybrid wires exposed to a magnetic field loop with constant sweeping rate. Comparing with bare Nb$_3$Sn and Nb$_3$Sn/Cu wires, we reveal two underlying mechanisms that the suppression of flux jumps is mainly attributed to the thermal effect of FM layer for the case of lower sweeping rate, whereas both thermal and electromagnetic effects play a crucial role for the case of higher sweeping rate. Furthermore, we explore the flux jumps of Nb$_3$Sn/FM hybrid wires exposed to AC magnetic fields with amplitude $B_{a0}$ and frequency $\rm\omega$. We build up the phase diagrams of flux jumps in the plane $\rm\omega$-$B_{a0}$ for bare Nb$_{3}$Sn wire, Nb$_{3}$Sn/Cu wire and Nb$_{3}$Sn/FM wire, respectively. We stress that the region of flux jumps of Nb$_{3}$Sn/FM wire is much smaller than the other two wires, which indicates that the Nb$_{3}$Sn/FM wire has significant advantage over merely increasing the heat capacity. The findings shed light on suppression of the flux jumps by utilizing FM materials, which is useful for developing new type of high-$J_c$ Nb$_{3}$Sn conductors.