Direct numerical simulations for non-equilibrium superconducting dynamics at the transition edge: Simulation for MgB ₂ neutron detectors

We perform large-scale numerical simulations on the non-equilibrium superconducting dynamics after a neutron capture at the superconducting transition edge in MgB ₂ by solving the time-dependent Ginzburg-Landau equation coupled with the Maxwell and the heat diffusion equations. The simulations are carried out under the current-biased condition in order to explain experimental results made in the JAEA reactor JRR-3, and the time scale of the obtained voltage signal is found to be almost consistent with the experiments. Moreover, the time evolution of the voltage signal is connected with that of the spatial profile of the superconducting order parameter.