Energy dissipation in lightning flashes

In this paper the amounts of energy dissipation in different stages of ground flashes are estimated by electrostatic energy considerations. In the analysis the cloud is modeled using the typical charge configuration given by Malan [1963]. The leader stage is modeled by a column of charge that extends from cloud to ground. The linear charge density along the leader channel is assumed to remain uniform or decrease exponentially with height. On the basis of the results, the energy budget of return strokes and ground flashes can be described as follows: (1) A typical stepped leader-return stroke process that neutralizes 5 C of charge dissipates about 5.5×108 J. Of this energy about 3.5×108 J dissipates in the return stroke stage, and 2×108 J in the leader stage. An unit length of the first return stroke channel dissipates about 7×104 J/m. (2) A typical dart leader-return stroke process that neutralizes 1 C of charge dissipates about 12×107 J. Of this energy 4×107 J dissipates in the return stroke stage and 8×107 J in the dart leader stage. An unit length of the subsequent return stroke channel dissipates about 8×103 J/m. (3) A typical ground flash with four strokes dissipates about 9.5×108 J. Of this energy 4.5×108 J dissipates in the leader stages, and 5×108 J dissipates in the return stroke stages. In our analysis we also discovered the following: (1) The charge that maximizes the energy dissipation during the leader stage depends on the charge density of the cloud. For the values of cloud charge densities measured in experimental investigations this optimum charge is about 5 C. (2) For a given amount of charge neutralization, a cloud flash dissipates more energy than a ground flash.

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