Numerical simulations of thunderstorm-induced corona processes near lightning rods installed on grounded structures

For the purpose of estimating the efficacy of a lightning rod, the current of a corona was numerically calculated from a rod placed (i) centrally on the roof of a vertical grounded cylindrical structure, a model of a man-made object, and (ii) at the top of a grounded hemispherical structure of large radius, such as a hill or mountain. The calculations were carried out for a slowly varying thundercloud electric field and when this field was enhanced by the charge of an approaching downward leader. In case (i), variation of the ratio between the height and radius of the cylindrical structure leads to a variation in the (a) corona current from the tip of the rod over a wide range and (b) distance from which lightning is attached to the rod. In case (ii), it is shown that, contrary to the case of rods installed on the ground surface, a slowly rising thundercloud electric field can be sufficient to initiate streamers and upward leaders from rods tens of meters in height installed on the top of tall, grounded, hemispherical structures. When the thundercloud electric field is enhanced by the charge of an approaching downward leader, the discharge processes near the rod depend on its length and the height of the tip of the downward leader relative to the top of the hemispherical structure, but are almost independent of the hemisphere radius.