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

Abstract

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 B0 is above the threshold value Bc, 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 However, if B0 is below Bc, the sharp-front diffusion wave theory is no longer applicable.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 B0, the critical temperature Tc, and the cold metal resistance ηs. The dependence of the velocity on these three parameters is analyzed in detail in this paper.