TRANSIENT EXCITATION OF A STRAIGHT THIN-WIRE SEGMENT - A NEW LOOK AT AN OLD PROBLEM

The transient excitation of a straight thin-wire segment is analyzed with the aid of a one-dimensional integral equation for the current along the wire. A new almost exact derivation of that equation is given, in which only the radial current on the end faces is approximated. The integral equation obtained turns out to be identical to the ''reduced'' version of Pocklington's equation. Based on this derivation, existing and new numerical solution techniques are critically reviewed. Pocklington's equation and Hallen's equivalent form are solved directly by marching on in time as well as indirectly via a transformation to the frequency domain. In the frequency-domain implementation, a fixed coarse space discretization is used for all relevant frequencies. For Pocklington's equation, a conventional moment-method discretization leads to a Toeplitz matrix that is inverted with Levinson's algorithm. For Hallen's equation, the Toeplitz structure is disturbed, and the frequency-domain constituents are determined with the aid of the conjugate-gradient-FFT method. To this end, initial estimates are generated by marching on in frequency and using a new extrapolation scheme. Illustrative numerical results are presented and discussed.