Model of Quench Development Inside HTS Coils Including Quench-to-Critical Current Ratio Evaluation

It is well known that the thermal quench current densities j_q in high-temperature superconducting (HTS) coils can considerably differ from the “critical” short sample current densities j_c(T, B) based on a definite voltage level, for instance 1 μV/cm. The ratio j_q/j_c (lift-factor) can be higher or lower than one depending on coil parameters. The reasons are smooth voltage-current curves and large temperature margins compared to low-temperature superconducting devices. Several approaches for the description of the quench development in HTS devices are known. However, they are either not suitable for windings with nonuniform magnetic field distribution or were developed for a particular HTS magnet in the limited range of its working parameters. In this paper, we analyzed the simple steady state model of an infinitely long solenoid with nonuniform radial distribution of magnetic field and temperature. It allows to evaluate the main thermal and electrical parameters of HTS coils in j <; j_q region as a function of the tape critical properties, n-value of the j - E curve, cooling conditions, and radial thermal conductivity in a broad range of their values.