Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in an conductor
Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in an conductor
Grants, I.; Bojarevics, A.; Gerbeth, G.
Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
Keywords: magnetic field
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AIP Advances 6(2016), 065014
DOI: 10.1063/1.4954400
Cited 2 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ-24605