electromagnetic field due to lightning strikes to mountainous ground

the produced electric and magnetic fields due to lightning strikes to mountainous ground are determined in this paper. for the sake of simplicity a cone-shaped ground with finite conductivity is assumed to represent a natural nonflat ground. by this assumption, we deal with an axillary symmetrical structure so we use the cylindrical 2d-fdtd to save the simulation memory and time, dramatically. the return stroke channel is modeled using the antenna theory model with fixed inductive loading (atil-f) which is appropriately incorporated into the fdtd algorithm. we have derived the updating equations of 2d-fdtd for distributed resistance and inductance in atil-f model. both the first and the subsequent return strokes are considered and their related radiated electromagnetic fields are determined and compared with each other. the fields are calculated at an intermediate horizontal distance from the cone-axis. the calculated results show that the presence of the cone-shape ground introduces an enhancement in electric and magnetic fields, for both first and subsequent return strokes. since sharper lossy cone means larger current density in the ground, the increment in the amplitude of the fields is inversely proportional to the cone-angle. a hump is observed in electromagnetic field waveforms because of the current reflection form joint point of the cone-shape ground and the flat ground beneath it. it is more specific in the subsequent-stroke fields. simulation results for different cone-height are presented. it shows that for small values of height, the results approaches to those of the flat ground.