EM fields generated by lightning channels with arbitrary location and slope

It is well known that lightning discharges follow a tortuous path; therefore, a general technique able to evaluate the electromagnetic (EM) fields associated with discharge currents flowing into tortuous channels seems to be worthy of consideration. Two techniques have been adopted to find the EM field generated by a current pulse traveling along a single line radiator with arbitrary slope and location above the ground. The first one employs the Fraunhofer approximation, which can provide useful information only on distant radiated fields. The second technique is exact, but applies only to the case of a velocity of propagation v of the current pulse equal to c (velocity of light). Even this solution is indeed inadequate for our purposes since v<c, as evidenced in the literature. In this paper, we evaluate the EM field associated to an arbitrarily oriented radiator without making any mathematical approximation in order to obtain closed-form solutions for the fields. A schematic square-pulse representation of the current and charge distributions along the discharge channels are adopted. The fields due to arbitrary time-varying sources are obtained adopting a suitable convolution integration