Transient response of very long cylinders through a new proper eigenvalue method

We present a new very efficient numerical technique for determining the electromagnetic transient response of very long cylindrical samples (length≫diameter), excited by an axial coil. The procedure is based on the interpretation of Cramer´s determinant rule as a generalized eigenvalue problem, whose solution provides the poles and zeros of the system. We illustrate the application of the method for the transient response of cylindrical samples with spatially constant conductivity and permittivity (with and without displacement currents), where we can compare standard finite difference numerical results, with the analytic and the proper eigenvalue solution. We present the computing time required for the different numerical approaches. We also discuss the conditions for the application of the eigenvalue procedure in the case of cylinders with radially dependent conductivity and permittivity (with and without displacement currents)