We construct magnetohydrodynamic (MHD) similarity rebound shocks joining `quasi-static asymptotic solutions around the central degenerate core to explore an MHD model for the evolution of random magnetic field in supernova explosions. This provides a theoretical basis for further studying synchrotron diagnostics, MHD shock acceleration of cosmic rays, and the nature of intense magnetic field in compact objects. The magnetic field strength in space approaches a limiting ratio, that is comparable to the ratio of the ejecta mass driven out versus the progenitor mass, during this self-similar rebound MHD shock evolution. The intense magnetic field of the remnant compact star as compared to that of the progenitor star is mainly attributed to both the gravitational core collapse and the radial distribution of magnetic field.
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