Macroscopically, thermomagnetic instability of superconductors is a competition between the nonlocal electromagnetic diffusion, the thermal diffusion, and the heat transfer to the surrounding coolant. 11,12 Thus, dissipative vortex motion often leads to avalanches of magnetic flux, which stochastically occur at the weakest pinning points near the edges of SC samples. Vortex motion locally heats the sample, which results in a decrease in the local pinning strength, which further facilitates the vortex motion and eventually develops a positive feedback loop and triggers instability. 10 An electric current or varying magnetic field applied to a superconductor exerts Lorentz forces on vortices, and the vortices are set in motion once the applied current or magnetic field reaches a critical threshold value. The vortices are initially pinned by defects in the superconducting (SC) materials. 8,9 Under an external magnetic field or transport current, vortices initially nucleate at edges and then propagate in the sample when the external field varies. 7 Among these, thermomagnetic instability induced by vortex motion is one of the most commonly encountered challenges for the application of superconductors. 6 The behavior of vortex matter determines the entire electromagnetic response of superconductors, including the magnetic field trapping ability, current carrying capacity, and operating stability. Most of the practical superconductors belong to type-II, in which magnetic flux penetrates in the form of vortices (or quantum flux lines) under an external field higher than the lower critical magnetic field, H c1. Superconductors are widely used in many application areas, such as high field magnets, 1 superconducting quantum interference devices (SQUIDs), 2 microwave resonators, 3 single-photon optical detectors, 4,5 and so on. Our results provide new insights into vortex dynamics and give a mesoscopic understanding on the channeling and branching in the vortex penetration paths in superconductors under AC magnetic fields. We have also found that the nanometer sized pinning strongly modulates the penetration of vortices and the vortex matter is highly correlated with the lattice structure of the pinning sites. As the AC cycle proceeds, the vortex penetration process gets more unstable. Pronounced hysteresis in the vortex dynamics has been found in the film subjected to AC magnetic fields. However, the rising temperature and jump size in the magnetization weaken as the ambient temperature increases. Under fast ramping magnetic fields, the increase in the temperature and instability in the vortex matter are more significant. It has been found that vortex alignment and repulsion play significant roles in the branching of the penetration trajectories of the magnetic flux. The influences of magnetic field ramp rate, ambient temperature, and nanometer-sized artificial pinning on the vortex matter are considered in our simulations. In this paper, the microscopic mechanism of thermomagnetic instability in superconducting films subjected to a transient AC magnetic field is numerically investigated by coupling the generalized time dependent Ginzburg–Landau equations and the heat diffusion equation. Thermomagnetic instability is one of the significant challenges for the application of superconducting devices.
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