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 However, if B0 is below Bc, the sharp-front diffusion wave theory is no longer applicable.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.
Highlights
The diffusion of a strong magnetic field in metals is one of the key factors that affect the results of magnetic-driven experiments
A simplified resistivity model is used to study the nonlinear magnetic diffusion wave when the vacuum boundary magnetic field B0 is below the threshold magnetic field value Bc
The velocity Vc depends on three parameters, i.e., the boundary magnetic field B0, the critical temperature Tc, and the cold metal resistance ηs, of which the dependence on B0 and Tc can be simplified to the dependence on the dimensionless parameter γc = B20/(2μ0Jc)
Summary
The diffusion of a strong magnetic field in metals is one of the key factors that affect the results of magnetic-driven experiments (such as magnetic-driven flyer and magnetic flux cumulation). The Joule heat raises the metal’s temperature and the resistivity of metal increases, which in turn accelerates magnetic diffusion and the Joule heat production rate This forms a positive feedback of magnetic field diffusion. While the massive Joule heating generated in the magnetized region accelerates the magnetic field diffusion, the high conductivity in the relatively unmagnetized region hinders it This results in the formation of a “nonlinear diffusion wave” characterized by a sharp wave-front where the magnetic field abruptly decays. Garanin pointed out that the magnetic field needs to be above a threshold value in order for the surface of the metal to be burned fast into plasmas This was verified many years later in experiments..
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