A nonlinear analytical procedure for electromagnetic transients in ferromagnetic shields

The effective application of electrically conductive, ferromagnetic materials for shielding under intense pulsed electromagnetic field conditions such as those associated with electromagnetic pulse (EMP), electrostatic discharge (ESD), and lightning has been hampered because there has been inadequate guidance for the nonlinear behavior that such materials exhibit. An analytical procedure has been developed that uses a combination of mathematical and numerical analysis to characterize the nonlinear electric field transients induced at the inner surface of long, thin-walled, cylindrical, electrically conductive, ferromagnetic shields by axially-directed short-duration surface current pulses along the outer surface. The peak value of the electric field transient and the time at which the peak occurs can be expressed in terms of effective permeabilities that depend on an applied pulse parameter that is a fundamental combination of the nonmagnetic problem parameters. The paper describes the practical implementation of the analytical procedure and discusses the results of numerical calculations for selected permeability representations