Q293 : Modelling Retardation Effects in HIFREQ/FFTSES
Question With HIFREQ and FFTSES, is it possible to take retardation effects into account when modelling a lightning channel as a current pulse?
Answer It is possible, although at present rather difficult, to model retardation effects in the CDEGS software. The simplest model that can be used to model a lightning channel that accounts for retardation effects is as follows: the current at height Z in the channel is given by the retarded waveform of the pulse at time T = t - Z/v, multiplied by some modulation factor which is a function of Z only. Any function of time can be used for the pulse (Double-Exponential, etc...), and any function of Z can be used for the modulation factor (typically, an exponential is used).
Unfortunately, there are some unphysical features in this model that makes it somewhat unappealing. The problem is that the leakage currents generated at low frequencies are very large, no matter what the modulation factor function is chosen to be. These very large leakage currents are the source of large potentials and electric fields.
It is possible to eliminate the above problem, although somewhat artificially. The trick consists in replacing the leakage current at 0 Hz by the value computed by HIFREQ in an independent run where the energization is done only at the top (or bottom) of the lightning channel.
Modelling the retardation effect itself is quite complex. The energization for every conductor used to model the channel must be specified independently, and this for every frequency! The precise form of the energization to be used for a conductor whose origin is at Z (at angular frequency Omega) is exp(-Z(1/Lambda - j Omega / v)), assuming an exponential form for the modulation factor. The frequency dependent phase angle is the frequency-domain version of retardation.