The second type of sharp-front wave mechanism of strong magnetic field diffusion in solid metal

When a strong magnetic field diffuses into a metal, the metal is ablated by Joule heating accompanying the magnetic diffusion process, and the metal's resistance changes violently with the fast-growing temperature. This results in the formation of a so-called "nonlinear diffusion wave" characterized by a sharp "wave-front" where the magnetic field abruptly decays. A metal has its own threshold magnetic field value, which is determined by the critical temperature of the metal. If the constant vacuum magnetic field B-0 is above the threshold value B-c, the magnetic diffusion process can be approximately described by sharp-front diffusion wave theory [B. Xiao et al., Physics of Plasmas 23, 082104 (2016)], which gives a simple formula to describe the velocity of the diffusion process. However, if B-0 is below B-c, the sharp-front diffusion wave theory is no longer applicable. In this situation, one would need another type of sharp-front diffusion wave theory (type II theory) to describe the magnetic diffusion behaviors. In type II theory, the sharp-front diffusion wave velocity depends on three parameters, i.e., the magnetic boundary condition B-0, the critical temperature T-c, and the cold metal resistance eta(s). The dependence of the velocity on these three parameters is analyzed in detail in this paper. (C) 2019 Author(s).