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

TL;DR

This paper investigates the early-time electromagnetic response of magnetic targets, revealing a multi-power law structure and surface modes that depend on the target's magnetic permeability, supported by experimental data.

Contribution

It demonstrates the existence of two distinct power law regimes in the early-time response of strongly permeable targets, extending previous work on highly conducting targets.

Findings

Identifies a crossover from $t^{-1/2}$ to $t^{-3/2}$ power law behavior in magnetic targets.

Confirms the theoretical predictions with experimental data from ferrous targets.

Shows the early-early time regime is very narrow for targets with high magnetic permeability.

Abstract

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.