Surface modes and multi-power law structure in the early-time response of magnetic targets

It was recently demonstrated [P. B. Weichman, Phys. Rev. Lett. {\bf 91}, 143908 (2003)] that the scattered electric field from highly conducting targets following a rapidly terminated electromagnetic pulse displays a universal $t^{-1/2}$ power law divergence at early time. It is now shown that for strongly permeable targets, $\mu_c/\mu_b \gg 1$, where $\mu_b$ is the background magnetic permeability, the early time regime separates into two distinct power law regimes, with the early-early time $t^{-1/2}$ behavior crossing over to $t^{-3/2}$ at late-early time, reflecting a spectrum of magnetic surface modes. The latter is confirmed by data from ferrous targets where $\mu_c/\mu_b = {\cal O}(10^2)$, and for which the early-early time regime is invisibly narrow.