Magnetic instability in hard superconductors

By considering the electric field induced by flux motion, the requirement for stabilization of a hard superconductor against flux jumps has been found to be $J_c^2{\mathrm{\hspace{0.17em}<\hspace{0.17em}k}}^2{C}_s{T}_0{\text{[1+(D}}_t{\mathrm{/D}}_m{\mathrm{)]\mu }}_0^{\text{−1}}$ , where C_s is the heat capacity per unit volume of the superconductor, T₀ is given by ‐ J_c(∂J_c/∂T)⁻¹, D_t and D_m are the thermal and magnetic diffusivities of the superconductor, respectively, and k² is the smallest number satisfying the following time‐independent temperature equation: Δ² (ΔT′) = −k²ΔT′. Using the above criterion, we derive the stability requirements in both adiabatic and dynamic stability limits. Then we discuss the stability of commercial superconductors covered by normal metal. The stability criteria can be obtained by replacing D_m in the inequality with the average magnetic diffusivity of the normal metal and superconductor.