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Le Vine et al. 1986
Le Vine, D.M., Gesell, L. and Kao, M. (1986). Radiation from lightning return strokes over a finitely conducting earth. Journal of Geophysical Research 91: doi: 10.1029/JD080i011p11897. issn: 0148-0227.

The effects of the conductivity of the earth on radiation from lightning return strokes are examined theoretically, using a piecewise linear transmission line model for the return stroke. First, calculations are made of the electric field radiated during the return stroke, and then this electric field is used to compute the response of conventional AM radio receivers and electric field change systems during the return stroke. The calculations apply to the entire transient waveform (they are not restricted to the intial portions of the return stroke) and yield fast field changes and RF radiation in agreement with measurements made during real lightning. This time delay is obtained theoretically in this paper. It occurs when both the effects of attenuation due to the conductivity of the earth and the finite velocity of propagation of the current pulse up to the return stroke channel are taken into account in the model.

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Journal of Geophysical Research
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