Abstract:
The problem of nonlinear magnetic field diffusion in a substance metallized by shock compression is considered. The problem is solved numerically for various time dependences of the current through the conducting region (direct current, linearly increasing current, and the current increasing as the square root of the time). Nonlinear diffusion leads to qualitative changes in the structure of the current in the substance being metallized. In this case, the maximal current density is shifted from the conducting boundary (at which it is located in the case of linear diffusion) to the bulk of the conducting material. For strong nonlinear diffusion and an increasing boundary magnetic field, the current density peak may approach the shock front. The numerical solution obtained here is compared with the analytic solution obtained earlier for linear diffusion.
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