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. An almost exact derivation of that equation, in which only the radial current on the end faces is approximated, is given. The integral equation obtained turns out to be identical to the reduced version of Pocklington´s equation. On the basis of 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. 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. Illustrative numerical results are presented and discussed